rhythm games are literally scoring your timings, a cinema offers no such equivalent of a scored feedback loop.
No, I wouldn't notice 3ms on the lips of an actor. Drummers are known to be able to perceive 1-3ms differences in timing; again, a tactile action.
If a human is involved in the action their sense of rhythm and prediction takes over to allow for manipulation within those timescales. It's not uncommon, either.
You are claiming that someone can tell the difference between playing the game oneeter or two metres from the speakers.
Put another way, on a large stage the sound from the bands monitors takes ~10ms to reach the drummer.
I don't have data, and neither does anyone else here apparently, but in the absence of evidence it seems exceedingly likely that any perceived differences due to 3ms latency (difference ?) are placebo. We know that placebo is real and large so unless someone has an experiment that tries to account for this (e.g. properly blinded) my prior is that you can't tell when playing a rythm game whether the speaker is 1m or 2m from you.
Like tuning strings by hearing when you can pluck both strings at the same time, vs doing it using absolute pitch.
I don't think we could tell direction based on the distance and less than 1ms difference alone.
3ms is how long it takes sound to travel a meter.
Do you notice the difference in audio/video sync between sitting in the front or the back of the cinema?