Okay, so, I am a gamer as well, but your Grey needs AT LEAST a few hours of direct attention daily. They need social interaction as they're highly intelligent and the more interaction they receive, they more cognitive they are and the happier they are.
That being said, when I game, Chance yells at me to "step up, now!" so I usually get her and she sits in the bed with me as I game. This is fine until she tries to bite the Wii remote.
Getting an African Grey is a rewarding experience like no other BUT they are indeed phobic (she gets night frights at times) and she is very demanding. You can't treat a Grey like they are a cat... Greys are basically feathered children with matching intelligence and needs. While Chance likes her space, even if she is perched on her orb she still talks with me. It is basically like having a conversation with a human being. I am not kidding. We talk and argue all the time, lol.
Chance used to wake me up but I wake her up now.

I spend the mornings arguing with her as I have my coffee.
They are also dusty, so you will not only need to devote your time to cleaning (I mop the floors every night) I also have an air purifier.