G4400 is a dual core and will have a problem with multitasking like streaming.
He needs sufficient ram also to keep all tasks in ram.
I think an upgrade to a quad, or at least a I3 will be more appropriate.
If the games are fast action shooters, then possibly the graphics upgrade would be good.
Have him run his games, but lower the resolution and eye candy.
If your FPS increases, it indicates that your cpu is strong enough to drive a better graphics configuration.
If your FPS stays the same, you are likely more cpu limited.