Depends on how the game is programed to sync itself, some are syncing off the bus/CPU speed others use game FPS or an internal tick timer, Bethesda games are horrible for syncing off the games locked 30/60 FPS and it wasn't till Fallout 4/Skyrim that they fixed this. The most well know example of a game needing correct speed would be Wing Commander which is notorious for not working well except on period correct hardware, though some have managed to get it working right with slowdown tools.

So depending on how the game works internally a slow down tool may help as the system gets closer to the speed the game is expecting or it may go the other way and break the game entierly. No idea if any one has any data on which game break or work with slow down tools but it doesnt hurt to play around and test for yourself.

Slow down tools can be "tricky" and cause unexpected behaviour,
especailly in DOS.

If the chipset supports it and if the tool knows about it, the
best say to slow down to change the CPU clock, disable cache and
things like that - things that which will affect the speed of
every instruction (changing cache has mixed results, but doesn't
usually affect things much)

Otherwise, you have to inject extra "work" for the CPU, but in
order to do that you need to interrupt the CPU - the obvious way
is via the timer "tick" which occurs at 55ms intervals.

A lot of DOS slow down tools will hook the timer tick and perform
a time-consuming loop every 55ms ... This has the effect of slowing
down the effective speed the user sees ... but ... in between those
55ms pauses the CPU runs a full speed - depending on how the software
works, this can cause "weird" behaviour.