There are a couple of stumbling blocks you may be encountering, but first, I'd just like to say, many children have to be taught how to either reign in their over-developed sense of everyone bowing to their needs and whims, or they need to be taught how to speak up for themselves. When these two extremes are balanced, it can be referred to as self-advocacy. Eight is a great year for learning about self-advocacy and your child will need continued support in learning how to self-advocate appropriately right through to adulthood so consider any answer, only the beginning to a journey and a process. I hope you will find at least part of this answer helpful in some way.
Developmental Concern About Fairness
At your son's age, an expectation of "fairness" is fairly standard and something that is highly important to many kids. My guess is he is under the impression that fair means "equal" and "same" (as many kids are) and needs to learn this is not really the case.
My attitude with my daughter has always been that life isn't fair. We are all dealt different cards and have different talents and foibles - this means each of us also needs slightly different things. I then draw from real-life examples to show her this.
One example I have used with her is I was blessed with a better sense of keeping track of the "to-do" list and managing priorities than my husband was. This means he keeps a running list in his phone (He is also a realtor) - I don't have to because I can usually remember better, so he gets the latest and greatest when it comes to phones - I don't because I don't need it. That means more of our budget goes toward his phone than towards mine and she knows that. She also sees me being completely okay with that. When I need it, I grab a piece of paper or my planner to write my lists. I only need my phone to text, make calls, and occasionally snap a picture (I prefer my camera for that last one). At the same time, I am the family record-keeper, so I have the computer with more memory, a better photo program, and the better camera. She knows that too.
A more solid "in" conversation example for a child might be, You like to practice Tae Kwon Do, but you don't like dance classes. Would it be fair if everyone had to take Tae Kwon Do? Would it be fair if everybody had to take Dance? Do you need the same things for both kinds of classes?
It will take many examples before the lesson really sinks in, but he will most likely get it eventually. Some of the other answers here offer you more, great examples of this even in the possible explanations for the examples you gave in your question.
Another developmental step that may be a block for your child
You mention not just rules, but also breaks in routine, some children have trouble with transitioning from one activity to another smoothly if it feels unexpected or out of control to them. We commonly see this in toddlers, but the challenge can linger longer in older children as well. My little sister had such a hard time with routine breaks that even into her teens she'd get a little constipated during travel, particularly busy months (like Dec. with its holidays, tests and everything), or just if things were out of kilter for her. Even now, change is definitely not seen as a friend by her.
Your kid may be one of these that just struggles with transition and change and needs a little extra support on this front. When a routine change is predictable and forseeable - talk with him about it in advance. Mention what will change, why it will change, and what the duration of the change will be. Remind him of the change as it approaches and then reassure him there will be a return to the routine in X number of days, minutes, etc. Give him an opportunity to practice self advocacy by asking him if there is one part of the routine he thinks could be retained for the duration of the break in routine that would help him, what would that be? Then do your best to give him that one thing if you can.
For the momentary breaks in routine - especially those that were unpredictable, there isn't a lot you can do except explain what happened to change things, reassure him when you will be back on track and expect everyone to move on (with a little empathy however that might look for your circumstance - a hug and "sorry", a pat on the shoulder with a look that says, "I know this is hard" - whatever.
A great way to go about this is to start with teaching your child about win-wins or compromise. The whole point of many rules (once you get past the ones designed simply for safety) is to help find a middle ground that provides the greatest good for the greatest number of people. That means if a rule isn't meeting the needs of some individual or minority group, that person or persons has a right to speak up with an alternative that still meets the needs of the other but also accounts for the minority needs - this is how negotiations can begin.
How this translates in the life of a child is again, to use examples and be for the parent to be willing to work with the child to find win-wins. You can use the quiet game instance as a wonderful example about this:
He reminded her that it was a quiet time and she responded that she
was practicing the song for the concert.
Ask him how he reminded her - there are ways to remind someone that are bossy and there are ways that are self-advocacy. "so and so, we're playing the quiet game now and I'd really like to be on the winning team, can you practice singing later?" would be a perfectly appropriate way to approach the singer in this situation that is exhibiting self-advocacy. If she were to respond with "I'm practicing for the concert and got permission." then he is made aware her singing won't count against him and all is well.
You then have to teach a child to go get help from an adult when they encounter a child that is simply unreasonable and won't budge (as it sounds the singing girl in the example may have been doing), but it is a place to start.
You may also want to make it clear to him that many of your rules are about safety but sometimes there is flexibility too. Invite him to self-advocate with you about things like bedtime, order of things in his bedtime or morning routines, which extra-curriculars he is doing . . . This will likely be a novel idea, so you might want to invite him to speak with you about a rule you already know he might enjoy a slight shift in to get things started. For example, I have made it clear to my daughter that her extra curriculars must include something physical (a sport or dance, something that moves her body and teaches her how to stay fit) and something musical. She can advocate for how to meet those requirements rather than me just insisting on a specific activity.
A good frame to teach kids to help them self-advocate constructively when approaching you or others is,
"I understand you want. . . but I would also like. . . can we try."
Great Resource for Teaching Self-advocacy and good habbits to kids
My favorite resource for teaching self-advocacy to my own daughter and a few of my students has been "The 7 Habits of Happy Kids" and "The 7 Habits of Effective Teens" both by Sean Covey. The three rules of self advocacy in the books are, "seek first to understand, then to be understood," "Think Win win" and "Play well with others." Each book talks about these rules (and four other helpful "rules for life") in an age-appropriate way and we've read the one for kids over and over again at our house. The 7 Habits of highly effective families is by the late Stephen Covey (Sean's father) and can shed some light on the ideas behind the seven habits or rules in an adult-centered way if you'd like to read it as well.
In extreme cases or if the problem continues into adolescence
Let me preface this by saying, I worked in a school for highly gifted children with emotional, behavioral and learning disorders for a number of years. I cannot quote online studies at the moment, but have some background training that causes me to add this last bit on just in case.
I have to say, this is one of those struggles I know can be fairly common so I don't want to alarm you with the next part, you know your kid. This particular challenge can also be symptomatic of emotional disabilities I have encountered. When this is the case, over concern for sticking to routine and/or an over-inflated sense of self-assurance in knowing what is fair or not carries on later in life and in a more extreme form with highly emotive responses when the child sees something as not being part of the routine or as unfair.
I don't know the extremity to which you are struggling with this one, but when I say highly emotive I really do mean extreme. This would be exhibited with jaw dropping behavior or ear-splitting yells, not just a sense of dissappointment and/or confusion. If there is an emotional disability present of which you are already aware, you may want to mention the struggle to your child's therapist or get an opinion from one on whether this is symptomatic of the issue at hand.
If you are not already aware of such a disability in your child, but the problem really does seem extreme, you may want to visit with a child psychologist and discuss it with a professional and see what he/she thinks. Again, this is if you think the problem is profound and extreme - remember this is fairly common in its milder form.
Expect to take the opportunity to give your child feedback about how he approaches negotiations for exceptions for himself and in how he tries to "enforce the rules" by pointing out shifts he can make in his approach that are softer and more respectful of difference for a long time forward. but I hope these first pointers give a good place to start.