For Flash games, I'd say to just make sure you've got at least 4 GBs of available RAM. They are huge resource hogs, and your game can easily suffer from choppy framerates if you've got other things running in the background.
I've been using this dual core for I think 4 years now, and I don't have a problem playing any of the games on King, WorldWinner, etc. at all.
For non-Flash games that you might want to play, such as Bejeweled 3...yeah, you'll need some real computer specs.
Jacob, aka Meikyousisui on King.com & Worldwinner.com