I do not think it has been proven. I only found this
one study that examines StarCraft 2 players and shows that "Looking-doing Latency" peaks at age 24. This may potentially be
related to reaction times but that hasn't been shown yet. Secondly, looking at the distribution of ages across the leagues, they are highly concentrated at the age of 24-25, with very very few players of age 30+ being included especially for higher skill levels (see figure). To me, this seems like potentially a big flaw in trying to find trends as the older samples are almost just outliers.
The article also states that these results could potentially be explained away by "cohort effects" and different playstyles of experts ( see the discussion section of the paper) though they think it's unlikely.
Ultimately, we need other research groups to use other methods (e.g., longitudinal studies), better samples, and maybe more refined ways of measuring the player's focus. Also, some more research needs to be done to correlate these looking-doing cycles to reaction times.
EDIT: Also, about the articles showing that football players lose offensive potential at the age of 30, I think that in order to say it's solely due to natural aging, you would have to take into account the wear-and-tear playing football does and how that affects play too. In eSports, this physical punishment doesn't seem to exist (i wouldn't think anyways)