I don't have personal experience with a situation like yours, but I've recently come across an article about aggressive kids and how parents can deal with them. I'll try to get the gist of it across.
The article states that aggression in kids is always a request for attention. The child wants the parents to spend more time with them, or to know that they care about him. The article also says that aggression in children might be a reaction to feelings of insecurity.
If that's right, then handling your brother should involve
Taking an interest in his life
Spending more time with him (this is possibly too late at 13, when he wants to spend more time with his peers instead)
Showing him he is liked
Making him feel more secure. This is done by providing clear guidelines as to what kinds of behavior are acceptable and which aren't, and defining and enforcing limits.
Taking an interest in your brother's life and spending more time with him shouldn't need any direction from random strangers on the internet; your family is best placed to determine how you do that. You write that your parents are extremely busy: If this isn't needed to ensure the financial survival of the family, they should rethink their priorities. A thirteen-year-old is almost out of their reach; something will have to change fast. Right now your brother is only making life difficult at home. If he doesn't learn to control himself at home, he might have to learn it from others, with much more dire consequences until he has learned.
Defining and enforcing limits seems like a real problem in your family, and I don't think the situation will improve without changing that. Letting your brother get away with everything is the worst thing your parents can do; your brother might interpret this as a lack of interest in him, and misbehave even more to cause a reaction.
Short of physically restraining him, which he knows my parents won't do, they have no options when he refuses to comply
There is a very large difference between physically restraining someone and physically harming him. Your brother is 13, so at least your father should still be capable of restraining your brother when he becomes violent. There is nothing wrong in restraining someone who becomes violent; on the contrary, I think it's necessary to keep him and other people who are present from harm. Your father doesn't have to hurt your brother, or demonstrate his dominance; he can simply grab him in a bear hug, or possibly pick him up and deposit him in his room. I don't think that's usually necessary with 13-year-olds, but if your brother reacts to the enforcement of limits with violence, I don't think there is much else your parents can do (but see below for nonviolent resistance).
He was watching soccer on the television and my dad asked him to remove a plate from his place at the table and he refused so after some shouting my dad told him to turn off the TV and go to his room at which point my brother again refused and continued watching TV until my dad stood in front of the TV and they had a little face off. End result was my dad giving up and my brother continuing to watch soccer with no plate removed from the table
what can my parents do to punish him for doing something [...] yet not letting him "win" all the time?
This shouldn't be about punishment and winning, but about showing that actions have consequences.
In any kind of leadership function (and especially as a parent), you need to be reliable. If you expect people to listen to you, you need to make it clear to them that doing what you say leads to better outcomes for them than not listening. This also means that you can't invent arbitrary consequences - they should simply follow naturally from your brother's behavior. For example, if your brother doesn't want to put plates away, not letting him watch TV is an understandable, but arbitrary consequence. A better way to handle this might be to simply let the plate remain on the table. Nobody else should put it away. Sooner or later he'll be disgusted enough with his dirty plate to put it away and get a fresh one (this might take a while, but hopefully he'll understand before the plate starts crawling).
It works with other things, too. If your brother doesn't want to clean his room and throws all his dirty clothes under his bed, then maybe he shouldn't be made to pick them up - but nobody else should do it for him, either, and Mom shouldn't go collect his dirty clothes to wash them. Sooner or later he'll run out of clean clothes. He might go to school stinking to high heaven, but I bet he won't do that for long.
What if he leaves his stuff lying around all over the house, and everyone is disturbed by it? You could stow it away somewhere he doesn't find it (or ultimately throw it away) - if he doesn't clean up after himself, well, it's a natural consequence that he won't know where his stuff has disappeared to. He can't expect you to put away his stuff for him, and he can't expect you to tolerate more of a mess than the other members of the family make.
If your parents really aren't willing to restrain your brother when he turns violent, they can try a form of nonviolent resistance. It's supposed to work in several steps:
Try to prevent escalations (don't get dragged into arguments or threats, wait until the storm has passed before trying to talk etc., don't expect to win, simply provide resistance)
Once that has worked a few times, tell him they are no longer willing to tolerate the situation
If there is a violent situation, your parents get help from someone your brother respects. This might be another family member, a friend of the family, or even a teacher. This help consists simply of telling this person about the situation, and the person then telling your brother that he/she heard about what happened, and that he/she doesn't approve.
Note that step 3 requires that your parents trust someone else to know about the difficulties they have with their son.
Don't be afraid of having children of your own just because your parents don't know how to handle your brother. If you spend time with your children and tell them what kind of behavior you expect from them early on, chances are they won't develop your brother's problems.