I absolutely notice when a game defaults to a resolution with 60hz refresh rate. It's not even so much a stutter or stall as it just feels "off" and then feels "normal" if I adjust the settings to 144hz.

Though I don't notice this when playing a game that has fps capped to 60, as long as the monitor is refreshing at 144hz still.

I've also had a few ms of latency adjustment make the difference between frequently missing notes and being able to sustain long combos in guitar hero or similar rhythm games.

It's subtle to the point where it's difficult to measure objectively (if it's even possible to measure something where subjectivity is built in like sensory processing), but based on those I think our temporal resolution is higher than 60 fps in certain cases.

Edit: Though I'm not sure I agree that the latency difference between an internal and external sound card will be very noticeable. I used a USB dual pre for gaming for years and never noticed anything off with it. I might try breaking it out again to see if it makes a difference in rhythm games.

What do eyes and frames per second have to do with audio latency?

The human eye can't see above 60fps!

That's true until you get into VR. Then 90fps seems to be the threshold.

I'll leave the rest to the audiophiles.