Taking Intel as an example, you'll find that the same or similar GPU is used as you work your way up the Core i7 range.That means that even if you do upgrade the processor, you won't get an improvement in graphics performance.
Here's a specific example: My HP Compaq NX 9420 laptop runs Windows 7 Ultimate.
It has AMD Mobility Radeon graphics with 256MB of VRAM.
WOW for example, which is really the only game on the list I play.
I play Dragon Age at times, don't think I'd be happy with using integrated graphics for that either.
In most cases, it isn't possible to upgrade a laptop's graphics card.
If you want better gaming performance, the only sensible option is to buy a new laptop.
Just because the game will load and you can "play" it, does not mean you want to.
You can get from Boston to NY on a mule, but would you?
To identify the manufacturer and model of the computer's video adapter or chipset, use the Direct X Diagnostic Tool included with Windows 8, Windows 7, and Vista.