Deus Ex Machina is a literary device whereby a seemingly unsolved problem is resolved by a new character, event, ability or object.
Deus Ex is a videogame whereby the player character resolves issues that were seemingly inextricable. So in the case of Deus Ex, the player character is the deus ex machina.
This ties in a lot to Warren Spector’s design philosophy. Stories that aren’t just told to the audience, but told with the audience. The game is called Deus Ex, because it is a deus ex machina that is missing a machine(or the closest human equivalent).