For framerate gpu usually does most of the heavy lifting. But a slow processor can slow down a powerful graphics card.
It's not super common but some games do have more logic running to burden your cpu like more complicated AI running on your machine. Or maybe if there's a ton of characters in one place in some mmos. Or to run anti pirating protection to slow down that happening until it does. Then they might patch it out.
Typically most games more directly benefit from a couple high speed processor threads rather than many slower because they are just designed to run that way on pc since not everyone had 4 or more cores. Extra cores will still help reduce the stress of anything you might have on the background. It's becoming more common for newer games and game engines to utilize a lot more cpu threads as of late though. That's mostly for newer triple A games. For older games if you like wanna push really silly FPS it's all about the gigahertz (basically).