Yes, I agree, change is coming, most humans are "un-competing" themselves into diabetes and hundreds of other forms of death, god forbid they go do an active sport because they might lose.
As for video games, yes, they are playing by themselves, are they not playing to WIN? Is the object of the video game to go around and work collaboratively with as many people as you can find?
"but it's still a fundamentally bad situation because it's based on the idea that not everyone can succeed"
No, it's not. It's based on the idea that if anyone tries hard they can win, and if you don't try hard you may lose.
I'm sorry, but it will always be the case that the people who work harder for things CAN and SHOULD have those things and the people who don't wont have them.
If you took all the money in the world and divided it evenly among every person (everyone wins the same amount) do you think that in a week everyone would still have the same amount? I'm sorry, but the idea of "everyone wins equally being the new way of thinking" just doesn't and isn't going to work.
If it was true, why would anyone try? they wouldn't, we'd all sink to the same level of mediocrity.
There are thousands of every day examples where thinking "everyone gets a prize for trying" just doesn't work. It is the de-evolution of our society. Humans are the only species who spend the vast majority of their resources fostering the weak instead of working to become stronger.
Your statement about competition and innovation simply isn't true. Calling something nonsense doesn't make your point valid.
"it doesn't change the fact that it doesn't have as many benefits as cooperation" - if you're going to call something a fact, please back it up with at least one statement that supports that.

I find it interesting that it seems in every place where a competition involves winning by being fastest, you call it "arbitrary". the concept of being faster, by human locomotion or by mechanical means is probably one of the oldest concepts we have. Even tribal societies have competitions, they are a mimicry of life and frankly a chance to practice useful skills.
I would find it hard for you to say you "practice parkour" without saying that you aim to be "faster". ""Er" implies more fast than something - presumably with your standpoint, yourself - but what's the point of being faster? Isn't that "arbitrary"? Wouldn't it be more useful in your life in this modern age if you spent that same time studying marketing or business or reading or helping the homeless?
Can you say that life itself is not based in competition? Are there humans that are vying for the same resources as you? How will you get those things that you need? Is it possible to do that in a collaborative society? I would argue "not any more" - there's too many people and not enough resources. Through technological innovation (probably from racing) we have put ourselves in a state where collaborative "tribal" living is simply not an option. That works when there are sufficient resources per capita, and clearly as we multiply ourselves into the billions the earth is simply not ready for that.
You may argue that being collaborative has more benefits than being competitive - but there is simply nothing to support that. If the goal is to improve something, competition shows which things are most improved, therefore lighting the way for how to become more improved. There is no collaborative model that supports this process. Can two people work together to lift weights so that both become stronger? Yes, but one person can't make the other stronger, only their own force applied does that. Can two car companies work together to make better brakes? In a sense they do, and their testing ground is the racetrack, and when one is better the technology gets adopted and adapted by others and the whole society advances.
Can you show me an example that is strictly collaborative (and has no competitive element) that works?