You can play Doom inside Minecraft using a virtual PC – Engadget

The mission to make devices play Doom has extended to gizmos inside other video games. Reddit user uDrunkMate has been successful (through The Verge) in playing Doom inside Minecraft thanks to a just recently established mod, VM Computers, that can run Windows 95 inside Mojangs creative title.
There are some compromises apart from having to play on a screen within a screen. You can also forget about playing Minecraft inside Minecraft in the near future.