I'm not a native English speaker. So just like any other people who speak English as a second language, I always want to improve my English. Have you ever seen any good game that helps people learn English? Do you have fun with it? Do you really learn something with it?
Have you tried Duolingo? It's great and while not strictly a game it does have game features that make it fun to keep going back to. It seems to be held in pretty high regard when it comes to being properly educational also. I've been using it to brush up on my French, I thought I'd forgotten most of what I learned in high school but it's all in there somewhere and Duolingo is really helping me refresh my memory of it.