Note that it will be hard to actually gain a user-ship on a new site you just created, it takes a lot of time, luck and work to make something like a successful games website, let alone Facebook. Facebook games is mainstream only because it's attached to Facebook. It might be a more convenient approach to start with convincing current popular games sites to add Bitcoin as a feature. For example, bitcoin100.org is doing this with charities.
There are some little games already that only accept Bitcoin or Dogecoin. My favourite is blockchain-reaction.com for Bitcoin. Note that they have a small, targeted goal. Choosing a niche is how they can gain a following quick - being one thing well rather than all things badly. This sort of thing is easier and fun to create. There needs to be something that a user sees as differentiating the Dogecoin sites from the others - that they can only get from Dogecoin - simplicity and casualness of transactions, a unifying art scheme, innovative game-play or a genre of gameplay, etc. A large number of these, and some marketing around them, or a unifying website, would be great for spreading the coin around.
Anyway, I'm all for promoting coins to be used as an actual currency instead of just investment. So is the Doge community. So good luck!
It would be difficult to get mainstream games to hop on the cryptocurrency ship seeing that the market can be manipulated so easily.