Can the Nyquist sampling rate also apply for the human eye the same as in electronics?

The firing of neurons in the eye is completely asynchronous, so for all intents and purposes, the process we call "seeing" must be considered continuous-time, not sampled. Nyquist does not apply.

If things move too fast, they simply appear blurry. And "too fast" varies from person to person; there is no well-defined cutoff frequency for the general population.

The terminology used when applying to the human eye is the Critical Fusion Frequency, also called the Flicker Fusion Threshold. This is the frequency at which a point of flashing light merges visually into a single solid point of light. The precise frequency differs depending on what area of the retina is being stimulated, how bright the light is, how much ambient light there is, and what wavelength the light is. At the lowest (dim, blue light, center of retina), the frequency can be as low as 10 Hz. At the highest, it can be over 60 Hz. A saccade (rapid eye movement) temporarily disables this limit.

This is not a limitation of the retina itself, but rather an intentional blurring that occurs in the brain called visual persistence, a phenomenon that allows us to process briefly-seen images for a split second longer, at the expense of lower temporal resolution. The reason subliminal visual stimuli work is because an image can be flashed slow enough that our retina can pick it up, but too fast for our visual persistence to kick in, leading us to have no conscious awareness of the image having been displayed. An image of a couple kissing that flashes for a matter of milliseconds will elicit positive emotions, despite the fact that our visual persistence does not give our conscious mind enough time to process the image and be aware of it.

For the human visual system, an excessive frequency will not result in aliasing. Aliasing applies only to a periodically sampled signal when the original signal contains excessively high frequencies. The visual system does not have a discrete sample rate. Blur will simply result from the previous images being superimposed over the current one as they reside in immediate memory. When the image changes too rapidly, it results in a blurred, confusing perception.

There is a known visual illusion where objects moving periodically at a certain frequency appear to be moving in the opposite direction under continuous illumination. There are different theories explaining such observations, and one of them suggests that human vision has what could loosely be called "sampling frequency", somewhere between 15 and 20 Hz. AFAIK there is still a debate on the matter, and since classic experiments on subjective stroboscopy involved taking LSD and similar drugs, experimental data in this area is far from complete.

What you will certainly not find is a sample frequency which is constant across population, different light conditions or even different parts of the visual field.