I think it depends really. A lot of old Dos/Amiga games relied on the cpu being the exact speed they expected, and would run at 1000x speed if you booted them natively with a modern cpu. But any modern PC game can account for different speeds since it runs based on system time or framerate.
I think most 3ds games don't rely on the cpu speed, since new3ds speeds through HANS don't break them. Maybe some DS games do rely on it, but it still sounds rare so far.
you know, most modern games (nes onwards) literally wait for interrupts for the next event, ie: most IO things work sync/async where the interrupt (the hardware that raised an interrupt has done fully cycle count of the target cycle time, given a base CPU/BUS frequency) across different perhiperals.
Plus the "frame sync" happens mostly on the video hardware, since it will make sure (given a preset frame per second interval) for the GPU to notify CPU (through an interrupt) when its time to draw that frame on screen (since the game wrote that frame long before this event, but STILL needs to render the whole frame before proceeding with the next one, so the game/code must wait for the frame to be drawn (wait for frame interrupt) )