Again, this is all entirely subjective, and highly subject to individual tolerance, among many other variables. There’s limited (none?) studies specifically on video gaming and caffeine, but, as I referenced already, various aspects of cognitive performance and other related parameters that may help with gaming performance may not reliably be improved without moderate to higher doses of caffeine in habitual caffeine consumers. There is no definitive answer here, so more options for the consumer is a GOOD thing.
Elsewhere, while not gaming, but since you brought up shooter games, let’s look at actual (or simulated) military use:
200mg caffeine given to prior to simulated sentry duty was able to reduce errors in discriminating between friend and foe, and abolished the reduction in speed of target detection with time during the sessions without negatively impacting marksmanship.
(Edit: link to said study is broken, was from an old post of mine years ago, I’ll try to link up as proper link that works)
If it doesn’t throw off actual aim with an actual weapon, and reduces friend/foe discrimination, perhaps the same may apply to gaming? Maybe, maybe not. Interesting either way.
There are several studies using 200-300mg for soldiers noting no decrease in accuracy, paired with improved reaction time, target acquisition, etc. I don’t think it’s fair to say that >200mg will inherently throw off your aim. How will this translate from a real weapon to a controller controlling a video game weapon? I don’t know, but it’s worth noting IMO.
But again, YMMV. There’s so much individual variables and variance in caffeine tolerance, that someone may not feel much of anything with 300mg, while someone else may get jittery with 150mg…