M&M1 and the early Wiz titles update when the game receives input. There might be an absolute upper limit to how often it can update the screen, but I don't think it really matters realistically. Though it's worth noting that the Apple II versions of Wiz 1&2 had very slow screen update algorithms, and took so long that you could actually lower the ingame draw distance to speed it up.
M&M2 has some animations at a varying but still pretty low frame rate. I'd guess that the upper range of frame rate is 15fps. The blacksmith seems to be hammering at around that rate, though most monsters move a lot slower than that. No idea if the input polling rate is faster than that or not.
It occurs to me that one could use a TAS-capable emulator to check this out. Play the game one frame at a time, and check which frames the game takes input on. If the game doesn't override the standard keyboard interrupt (does it?) one could even check the keyboard buffer to see when key presses are removed from it.
Speaking of Tool Assisted Speedruns, the absolute upper limit on screen updates could actually come into play, especially if it's lower than the limit on how fast the game can accept keyboard input. Basically, in a TAS input will need to be entered on the earliest possible frame unless some RNG manipulation is being done (and knowing these games, RNG manipulation will be important).