I used to have same problem as your son when I was a child, and now my nephew (he's also 7 and we're scarily alike) also has similar behavior, and not only in sport.
Obviously, I can't talk for your son, but I can tell you what the problem was/is for us.
We love sports. We're good at it. And the main thing - it's easy for us. Even hard work with endless line of training and exercises is easy, because result/progress/success is seen relatively fast after that. Me and my nephew also don't really have problems with communicating to other people on the level we need, and with studying - when we really put an effort into thing that needs to be done, and not being an endlessly lazy slouch, we have some result - sometimes exactly what we wanted, sometimes not, but still.
Thus, it's really easy to think that world around you mainly just goes your way. And it's really frustrating when it's not. Even with the simplest and littlest thing. Even if deep inside you know that everything is okay. Especially when something goes wrong with the things you care deeply and passionately about.
Notice, please, that such behavior is not unusual for a children at the age of 7 (and for teens, and for some adults even:) - often there weren't enough time for the nurture to overcome nature completely. Kids-extroverts usually very expressive with their bad mood, especially in sport - activity with high level of emotional and physical charge.
My mother talked to me, and helped me figure out and see the difference between justifiable cases that offended me, and things that annoyed me but really wasn't anyone's fault. Like, if some referee made a mistake - I need to remember that people is not working robots without bugs, so the referee can't possibly be perfect and see everything: thus I need to try and explain his mistake to him, if he's not listening than he's a rtick (my mom didn't use this word, but she explained to me that sometimes people just plainly dump and acting bad, and you can't do anything to fix it) and I should complain to the officials later if that's possible, anyway - it's okay to skip it and go on. If someone pushed me on the play field and did it unintentionally, it's okay to skip it and go on (if them pushed me intentionally, that's the whole other matter about dealing with bullies). If I can't master something on the first try - it's okay... etc.
She also taught me to channel excessive frustration into something (like shouting or some exercise if possible) or trying to calm down first: reciting poem or counting in my head, or remembering something - to distract myself in any way I find suitable. Even if it's image of offender dying painful death (joke... almost.). She told me that it's okay to take a timeout, calm down and return to the task/dialog after a while. That's not really works for the game, but it really helped in the beginning - just the possibility to go out, relax a little and go back.
My old coach helped with all of that a lot, because he has very strict policy about discipline: means, "if you have enough energy to throw a tantrum, you surely can run a couple of circles around the field, so feel free to do so. Also, you can return to training only after finishing this task." He stand to his words - if we couldn't finish our 'penalty' before the end of the train, the next one started for us wits completing the rest of the punishment first of all. Somehow along the way all of us agreed that showing everyone around your dissatisfaction is really cool, but definitely not worth a fifteen around the field, so... it's okay to skip it and go on. :)
Mainly it's all about dealing with stressing situations and finding the right way to process this stress and move on. Wrong way to address the issue is "sportsman wouldn't act like this" or "man wouldn't act like this". Decent human being wouldn't act like this. It's cool to be cool because freaking out about everything makes you unhappy most of the time. If your son has trouble with competition and losing - make sure to explain to him that sport is not about besting others - it's about breaking
your boundaries, beating your scores, being stronger, faster, smarter today than you were yesterday.
Also, if it's possible, I'd strongly recommend to talk with the coach(es). They could have some insight into the behavior of your son, some advises about helping him, maybe even change somehow his training routine - group he's in, his usual opponents/teammates, maybe give him some individual exercises or helpful tips. Usually for kids their coach is a strong role model, especially if there are no other fatherly figure in his life.
I do not recommend discipline him authoritatively with punishments for his tantrums. That'll make him feel like he's punished without a reason, no matter what the real situation is, and only motivate him to antagonize you; that'll make you the bad guy who doesn't want to understand him.
(Maybe combine? He realizes that his tantrums is not nice behavior, so you can involve him into process of fixing it: choose the evening, sit with him and write down a chart, like 'fault: penalty' . Even better if it won't be only about him and his unsportsmanlike behavior. Set out some kind of house/family rules, by which you also could 'get in trouble', so he'll see that it's not about punishing him but about both of you improving yourself with the help of each other instead, like 'family unit training plan'. It could also be useful in future with questions about homework, chores etc.
If he set the punishment himself (it really sucks for a child, honestly, because: ) he can't even complain about overly strict and unfair mom. He did it to himself - he behaved badly and he got the punishment he chose for this bad behavior.)
The saddest thing about situation is that there must be involved a lot of talking (reasonable and consequential, you must stand for your point with no backing up option), maybe adjusting/fixing some of your own routine (friendly reminder: in the matters of general human decency points like "I can do so (/ I am doing it) because I'm older (%whatever thing about age, position, earning money for family%)" (aka 'do as i say not as i do cause i said so') - are screwed up and good only for making children hate their parents), and it'll take a lot of time for him to understand the faults of his behavior, find and accept reasons for it and work out suitable ways to fix it.
Good luck to both of you.
UPD: about laying on the ground/standing at the sidelines - you can tell him that by doing such 'protests' he only wastes his own time. My nephew (and I, ages ago:)) used to do such 'strikes' to get away with skipping his homework. Now his playtime starts only after all the homework is done, right before he goes to bed. Discovering that he could stay past bedtime for homework but not for playing was really painful hit for the little guy.) But he started trying, at least.