What was the point of the game in Future Diary?
You're completely right in the reasoning that Deus is looking for a successor, and that is what happens in each case of the game playing out.

The survival game the anime covers is that of the second reality, which Yuki ends up winning. What isn't revealed until near the end of the story is that there was initially a first reality with it's own survival game, which Yuno won.

In the first reality, Yuno becomes so close to Yuki that after he dies and she wins, she can't bear being alone without him, so abuses the powers of the first reality's Murmur to enter the second reality to be with Yuki once again. Her plan was to do this repeatedly, winning the game in multiple iterations over numerous realities to be with Yuki for, essentially, eternity. Of course, this comes to a halt after the initial victory, as Yuki wins the second game.