Chess, after all, is a classic domain where expert performance is the result of intensive practice plus quality feedback (informally, the "10,000 hour" rule).
Computer chess plus the internet has made training better, cheaper, more accessible and more intense.
So nowadays anyone with any talent at the game should be able to progress faster than in the past.
I don't think chess was chosen because it's the best proxy, I think chess was chosen because of the sample size and data available about players and games and an almost quantitative model of performance during each game (optimal moves). Poker would also be valid or sudoku or many others but there's usually a certain amount of chance involved in most other games and the impact of that chance is hard to estimate.
I appreciated them focusing on chess exactly because of the third point you mentioned. It's a fairly even playing field in terms of learning opportunities.
I'm not sure why you think it's a bad example of cognitive performance. Reaction time is a type of cognitive performance. I am not sure how time taken to move was incorporated as a signal used in the methods in this paper but how quickly a person is able to play an optimal move is just as much of an indicator of cognitive performance as finding the right move is. Adrenalin control is also about being able to focus and getting in "the zone" and that is very much a proxy to cognitive performance. And to a certain degree, it's very much not controllable at all on a conscious level, but you get the same "rush" in chess when you worry whether an opponent is going to see whatever tactic or strategy you're pursuing in a game. And I'm not sure what you mean by extreme physicality, do you mean having to keep (arguable unhealthy) weight standards or do you mean the G-forces the driver undergoes?
In my opinion the cognitive load of racing at those high speeds is just as taxing as chess, maybe different learned skills are empathized. Other than extreme physicality, Bullet and Blitz chess require reaction time and adrenalin control too.
It seems that the range can only be generalized to a society/population level, since chess was used as a proxy and there's a lot of things that can shift the "peak" at an individual level. It can also vary based on how solved the game is, for example go vs chess vs tic-tac-toe.
It is interesting to see it was a bigger range at a point later in life. But I can easily think of things like formula 1 where the age of the peak performer has slowly shifted towards younger drivers simply because the drivers get into go kart racing and work their way up to formula 1 faster.
Regardless, it seems like a promising study to demonstrate that it's never "too late" to improve yourself, which is a problem people start feeling in places like the tech bubble where age is intentionally or unintentionally used as a signal for findind a good candidate. And the "too late" sentiment also comes up when people decide to get into things like chess later in life.
The the flattness of the curve seems like a double edged sword, it means time to reach peak has no special technique to accelerate when you reach a peak or how long you stay there, but it also means as long as you started with a proper foundation, your performance will decline is a lot less than the lay person would imagine.