Few DOS games will behave correctly if the refresh rate of the video modes is changed from what the games expected to set up. This is not due to the games somehow having had "bad programming", rather because DOS games had such small resolution, like 320x200, and there was no possibility for subpixel precise rendering/filtering.
Therefore it was often important to establish in game logic whether objects would move one pixel per two frames, one pixel per frame, or 2 pixels per frame, for example. I.e. there exist only very few "nice" object animation speeds that will be pixel perfect and look smooth and pleasing in panning motion.
So to get smooth animation, the animation speed must be fundamentally tied to the refresh rate when games have a very small resolution, like 320x200 or 320x240.
In (ViewTOP) WD90C30-LR ISA VGA DIP switches: play DOS games at 90hz refresh rate I found one DOS VGA graphics adapter that supported "forcibly" bumping up the refresh rate of graphics video modes, and tried it out on a couple of DOS games. The results were:
- Jazz Jackrabbit: 60Hz -> 75Hz upgrade: gameplay speeds up by that factor of +25% making it unplayable fast.
- Pinball Fantasies: 70Hz -> 89.457Hz upgrade: game logic runs faster by that factor.
- Psycho Pinball: 67.449Hz -> 85.634Hz: game gets confused and becomes -30% or so slower in slo-mo fashion.
- Pinball Illusions: 70Hz -> 89.457Hz: game logic speeds up by that factor.
- OMF 2097: 70Hz -> 90Hz: game logic speeds up and becomes unplayable.
- Lemmings, Xenon 2 Megablast, Prince of Persia, Commander Keen 5: 70Hz -> 88.118Hz, but gameplay speed did not become impacted, and were playable at the higher refresh rate as well.
So from this data one can see how it very much depends on the DOS game whether it would work or get confused if the refresh rate is forcibly changed on the game.