While the CPU is an important part of any computer when it comes to gaming the most important part is the video card. The video card determines what resolution and settings that you will be able to play at. The CPU then comes into play in a supporting role to help that video card with the settings and performance. The screen size is not the determining factor, the screen resolution is.
What is your intention here, to be building a computer or upgrading an existing one ? What sort of budget are you working with for components ?