The idea of being able to use Bitcoin in games is fairly mind blowing, once you start thinking about the possibilities. Build a house in one game, trade it for armor in another.
I'd start playing Magic: The Gathering again if the digital cards I bought were colored coins or counterparty-style tokens that I controlled, and could trade outside of the game.
If the game itself was open source and p2p, even better - there would be no worry of the company shutting down the servers/abandoning the game. The community could take over and make improvements to the client if needed. The initial creation of the game would be funded by selling the digital cards.
I think every card they print will eventually be represented as a member of a blockchain.
But what could we call such a site?
We're (I'm the founder) doing what you've outlined. Though the Deckbound-specific games are proprietary, the APIs and services are open -- and you can use the Deckbound card identities to make your own games. Ultimately we plan on p2p game clients as well -- and are building on top of other projects to deliver that.
G.
The initial concept is focused on Trading Card Games and built on the Bitcoin blockchain, but there are very interesting medium-to-long term plans that are very much in the spirit of what you suggested.