Thinking about it, 24fps (good old fashioned film), even though laughably low by the standards of modern displays, manages >1 frame per perceptual time-quanta, which is enough to give the illusion of motion. Any lower than that, and you start getting "frames" where there's no change in the film frame, and the motion illusion breaks down.
a) 24FPS are easily detected as flickering; our true flicker fusion frequency is found around 60-80Hz.
b) Perceptual time discretisation heavily depends on the modality and even the task in question. For motion extraction, this "limit" may be much lower or higher than for olfactory tasks or memory retrieval. Overall, it's really hard to put a time delta on neural processes -- after all, biological systems are more or less continuous.
Shooter player here. This is a laughable statement. Pretty much anybody can tell the difference between 60hz and 120hz - even the mouse cursor moves smoother. Good players try to play at higher than 120hz rates, because it does make the difference.
If the mouse were moving continuously you would be able to see the full trace of its path and not just a few discrete locations along the way. A higher frequency would get closer to this.
Also, in an interactive scenario, the frame rate will impact how quick you get feedback on your actions. With 60Hz, the frames each take 17ms, meaning the next frame will be on average 8.3 ms away. Thus if you perform an ingame action, you will get visual feedback in ~8.3ms, whereas with 120Hz it will come in 4.1ms. There is probably some kind of buffering done, so likely your action will not end up in the currently drawn frame but the one after that. So the response will on average come 3/2 frames after your action: 25ms later for 60Hz v.s. 12.5 ms for 120Hz. 10ms faster reaction time should be noticeable.
It also depends on darkness and color, so I really doubt the eye's fps has anything to do with the brains perception of time.
Here's a great article on this subject: http://www.100fps.com/how_many_frames_can_humans_see.htm
Games are essentially sampled screenshots. With virtually no hints as to what happened between samples. Just, in one frame an item is in coordinate X. In the next, it is in Y.
Movies, on the other hand, were not discrete samples of time. If between frame A and B, an item moved between point X and Y, then it will leave a blur between them.
That is, the information is distorted, but it is there. Unlike the discrete sampling where the information is just lost.
Shutter speed is different from framerate.
In high light situations, you won't end up with (much) motion blur.
The takeaway is that the perceptual frame rate for brightness is higher than the perceptual frame rate for motion.