Outside the game = from the sideboard, or elsewhere, if it's a casual game.
I would probably have named it "Emrakul's _______", but It that Betrays has set the precedent for an Eldrazi not being named after one of the Three.
The concept here is that this thing exists outside of the normal flow of (the many-worlds interpretation of) time. It enters alternate timelines by eating through them, and its physical form fills the gaps it consumes as it still exists in that timeline. When it leaves, the hole tears apart the connection between the past and future of that line, destroying it and collapsing the entire wavefunction at that one point. Where previously an event in time might have produced many different results, those that have felt the influence of the Gorger can only yield one inevitable fate (the one in which you, the observer survives rather than the versions that were erased with all of the alternate lines).