I think a person who overthinks does it regardless of the stakes. Focus is very closely related to not getting interrupted by your own thoughts. I agree with you that you need to have the skill to be able to perform well, but I'm suggesting that even in a low-stake one, one who can't focus won't focus, be it overthinking or distractions.

I learned this from this brain exercise game, Peak. I started leveling up like crazy when I stopped thinking and speaking to myself and let my brain do what it does best, which learning.