Winning Condition
There is no winning condition on Dimensional Rift - you win when your opponent loses and you don't.
Losing Condition
Any player loses the game if they reach 0 life points.
If the condition happens during the resolution of an effect, the whole effect must be resolved (not other effects in the chain though).
If a player then matches the losing condition, and the other player doesn't, the later wins the duel. If both players lose at the same time, the duel is a draw. (Luan's note: I don't know if this is currently possible).
There are no wining conditions or alternative losing conditions on Dimensional Rift.
You do not lose if you deck out. You are just unable to draw and will quickly run out of resources.
If both players deck out and reach an immutable game state, it is also a draw.