Other than the sun, are there any stars that should take up multiple pixels at the angular resolution available with current display technology?
The Oculus Quest 2 has a horizontal FOV of 97 degrees. In order for α Centauri to cover two pixels, you would need a display with 6.2179487x10^26 horizontal pixels. 621 yottapixels. Something like a hundred sextillion times "4K" resolution. And that's linear resolution, tag on some more orders of magnitude for display area.
There is a reason parallax is used to measure distance to stars, rather than directly measuring their visual diameter.
Even in outer space, with no atmospheric aberration, there will be some blur for anyone with less than absolutely perfect eyesight.
There will be a point-spread-function because our optics are not ideal (especially with bright point sources), and blur will result from a variety of causes.
Computer graphics are meant to be perceived through human eyeballs. So we can count on the eyes continuing to blur point lights whether you're looking at a screen or at outer space.
Also, the game might be simulating an experience from a character's point of view, and expect the player to be wearing glasses to correct their personal vision defects (to the extent possible).
(The calculated horizontal resolution required for a 2 pixel wide star from the original post should instead be 100,009,624)
The corrected number for star apparent diameter should be 0.006983 arcsec. Depending on how finely you want to resolve the disk, that would take somewhere between a 70 to 140m wide telescope. (With 400nm light)
The largest optical telescope currently under construction is 39.3m wide: https://en.wikipedia.org/wiki/Extremely_Large_Telescope