Why does Khan want revenge? It's said he wants revenge for Kirk marooning him/death of his wife, but Kirk marooned him there because of Khan's attempts to take over his ship.
It's Khan's fault he was left there. He started the whole thing. He has no right to seek revenge when it's his fault in the first place!
Khan was vengeful because, as he said, "Admiral Kirk never bothered to check on our progress." If Kirk, or Starfleet, had monitored the colony, then they would've detected the disaster, provided aid, and maybe been able to prevent Marlena's later death.
Besides, Khan had been living in hellish conditions for years, enduring the grief of losing his wife and nineteen others of his people. That's plenty of time to nurture a grudge into an obsession, to get fixated on an idea even if it isn't objectively reasonable. He wanted someone to take out his rage on, someone to punish, and Kirk was the most convenient target.