First combat damage is assigned. After that, creatures go to the graveyard (if they've taken lethal damage) and then 'dies' triggers will trigger.
So if you're doing lethal damage to your opponent in combat, the game will be over before the Cuddling Doom Engine's trigger goes off.
December 16, 2014 12:56 a.m.
You'll win, the triggered ability of Scuttling Doom Engine won't get get on the stack, much less resolve.
A player losing the game due to 0 or less life is state-based action. State-based actions are checked every time right before players would receive priority. Scuttling Doom Engine's 2nd ability is a triggered ability (because it uses the words "when/whenever/at") so it must go on the stack to resolve, but it never will because state-based actions have already been checked an your opponent has lost.