There are multiple factors that affect the accuracy. The most obvious is the precision with which the features are localized in the image. I use the term "optical gain" to describe the number of pixels of image movement of a feature for a given amount of eye rotation. Clearly more pixels on your sensor helps, as does a lot of optical magnification. Best results will be obtained when the features of interest fill the entire sensor area, but of course that limits the amount of allowable head movement, so there is a trade-off. You can eliminate a lot of problems by stabilizing the head - or putting the camera on the head, effectively stabilizing it as long as there is no slippage.

When I got started in this business, using NTSC cameras, the best we could do was about 1 pixel of pupil image movement for 10 arc min, or about 0.15 deg. The optical gain of the CR is somewhat less. It helps if you can locate the features with sub-pixel precision.

The second factor is what you do with the measurements once you have them. The design of the DPI tracker uses collimating optics to put the source and detectors at optical infinity, with the result that P1-P4 cancels out all of the head movement. This is not the case for most video setups; the correct way to combine the measurements involves geometry-dependent formulas to recover the orientation (and position) of the eye. There is a 2006 ETRA paper by Kolakowski & Pelz which goes into this.

The questioner mentions variation in pupil center position with pupil size. There can be subject-dependent physiological effect (which might be calibrated on an individual basis), and there are also geometric effects. The apparent center of a perfectly circular pupil constricting in a concentric way will be stationary when the eye looks straight at the camera, but not for eccentric gaze. (I modeled this in my own 2006 ETRA paper.) This can be well-compensated for if the optical parameters of the eye are known.

In principle, I don't see any reason why a video-based system couldn't approach the physiological noise floor some day, although I haven't done it yet. Rather than relying on P-CR to cancel head movement, it might be better to track non-eye features like the canthi (eyelid corners). People have also put markers on the face.

It's been suggested that one could apply higher optical magnification to features much smaller than the pupil, such as scleral blood vessels. One problem with that approach is that as optical magnification increases, depth of field decreases, so it is hard to hold focus as the eye moves.

It is surprised for me how once can use the eyetrackers with accuracy 0.5 deg. for the detecting microsaccades.