Is hard disk also responsible for game performance?
A hard disk is responsible, but only in a few specific ways:
Loading times. The time it takes to start the game, or load resources from disk (for example when entering a new map or region) are directly related to Hard Disk speed. If you've ever played on a machine with an SSD, you'll know all about this. Hard disk performance is the bottle neck here, so however fast your machine is otherwise, loading time will be governed by your Hard Disk speed.
Auto-save lag. This works in the same way. If you have a game that auto-saves regularly for you, a slow HDD could cause extra lag when this happens, although this depends on a few more factors too.
Paging/Virtual Memory. If you're on a machine with a low amount of RAM for the game you want to play, some of the game may be loaded into virtual memory on the Hard Disk. This will nuke game performance, as reading/writing from disk is about
100200,000 times slower than from memory. Check your memory usage when you're playing your game, if it's very high then your machine might be putting some of your game's resources in virtual memory.
The latency of RAM compared to a Hard Disk is visualised nicely in this image (zoom all the way in on the top left of the image).