Windows would not allow you to format that way. When You format your windows partition (drive C), you need to do it during boot. Of course then you have to install the operating system right after. Of course you loose everything if you do not back up, as you've said you do not have anything important, then that would not be an issue.
I do not recommend reformatting though. Just remove any programs you do not use, delete any files that you do not need. Truth be told, it is doubtful your gaming issue is yet your HD. Yes windows hates a full drive, but you still have a considerable amount of space before Windows shows signs of slow down. When you are down to about 2gb's left, then start to worry. I just mentioned it because it is good practice to remove unneeded junk.
If your PC is showing signs of poor performance, then try removing spyware and scan for virus's. Remove the sides and see how dirty it might be. A dirty computer can overheat and slow down. It is always a good idea to check for updates for drivers etc. If there is a considerable amount of dust build up inside, use a can of compressed air to blow it out.
Edit:
Did you check your video drivers settings? are they set for best performance?