I think it's important for kids to play with a variety of types of friends/relatives. Sometimes they're going to win, sometimes they're going to lose, sometimes they're going to learn that keeping score isn't required in every aspect of life. It's great that you don't want to be a helicopter parent because that really handicaps kids and makes their self-esteem even lower ("because I can't do it without Mom and Dad..."). So instead, work on giving him not only th coping skills but also the values to understand the downside to being competitive. Do you play family board games that rely on cooperation or team-building? When I was a kid, we played "Monopoly" (the world's most competitive, and interminable, game) cooperatively, with trades and ways of helping out (putting taxes and fines in the middle of the board, where they could be claimed by anyone landing on "Free Parking", or giving $500 for landing directly on "Go" and so on). We didn't want anyone to go bankrupt. If we traded properties, we gave the "poor" player a lot of chances to land on the resulting hotels for free. That sort of thing. Yes, it was fun to make money, but it was no fun to watch anyone suffer or have them drop out of the game and only be able to watch while the others kept playing for an hour. Or three.
I wouldn't speak to the aunt/uncle, because you admit that your child can be very competitive. Teach your child ways to say, "I don't like this, let's do X instead" or even "I used to like wrestling, but I'm not interested anymore." Find some games that involve fun for everyone, and ask your son why it's only fun when one person wins. Help him be more compassionate towards the child who isn't as fast as he is, even if the cousin is faster. Develop, and celebrate, other interests so that physical prowess isn't the only measure of a "champion." Yes, he might want to do it when he's older, but then again, he might not want to do it at all, you know? Your nephew is eventually going to find someone much larger, stronger and faster than he is, and then where will he be.
But, it's okay to lose sometimes and still be a good sport. He's going to participate in gym class and he's not going to be allowed to opt out. He may perhaps join a team outside of school, and he's not going to hit a home run every time. But defense is important, team attitude is important, etc. Sometimes kids learn those values in another type of structured program, like tae kwon do. But I say that as a parent of a child who was not on teams (other than town recreation soccer or basketball teams now and then) and who didn't take karate or tae kwon do. He was the kid in the neighborhood riding bikes and organizing frisbee games and collecting groups of strangers on the beach to build a sand castle with lots of decorations and a trench to the ocean. Those are skills too. He found his passion of distance running, but not until 9th grade.
I think, if you balance out the cousin's intensity with other types of kids, and if you focus on "that's what's important right now to your cousin, but it doesn't have to be what you value," you will do a lot to encourage a more confident and well-rounded child. It's okay to start asking him age-appropriate questions, like, "Why is it important to be the strongest and the one who wins at wrestling?" Then listen to his replies.
And I do think it's too soon to worry about what will "hinder him for life." I think your own anxiety over this issue will be a bigger factor, and I hope you do what you need to in order to control your stress and worry. If that means some short term counseling, do it! It's a great gift to yourself as well as your son if you can clarify what's really important as well as get some help finding the right words to express that.