INSTALLING a game (or any other program) will have little or no effect on the performance of your PC. A program (or game) just sitting there on the hard disk is using no PC resources.
What does slow a PC down is when a program or game is RUNNING.
Any program or game running (including Windows) is loaded to memory, and the more programs in memory the slower the PC will get.
So you need find out what programs are running, and see if there are any that are not needed.
This is not always as easy as it sounds because Windows runs all sorts of programs just to keep Windows going and you cant just shut them down as you have no idea what effect that may have.
So shut down any obvious programs that you are not using. So dont leave Word, Excel, your browser and a game or two all running as they are using PC memory.
The best way to speed up a slow PC is to add more memory (that is real memory or RAM, not hard disk memory)