Nope. It takes completely separate circuitry to do video input as compared to output.
But if you have an older 27" iMac (the one with just-plain DisplayPort, not Thunderbolt,) you can do DisplayPort-in, which can be adapted with an active adapter from HDMI to DisplayPort.
You could use an Elgato
EyeTV HD or
Game Capture HD, but both of those add enough delay that playing games would be difficult.