However, we don't see immortal war-leaders.

Many (probably most) games with character avatars do have defeat/death conditions, so I don't see how this affects the probability in question.

So, if our God wants a persistent identity throughout the game

You've not listed this criterion in your sequence of conditional probabilities. It ought be something P(single persistent identity|ego, ent, sim, Earth) - and then we could debate P(chr0|single persistent identity, ego, ent, sim, Earth)

Also Jesus Christ wasn't immortal either, the fact he died is part of the core points of Christianity.