Both words being made famous by the Holy Bible, I'll use a slightly biblical interpretation. The Apocalypse is name given to the actual event itself, but Armageddon is where it takes place.

Apocalypse is Greek for "revelation" and Armageddon is derived from Hebrew, "Har Megiddo" or Mt. Megiddo where many battles took place. People use the term apocalypse and armageddon interchangably, despite them having different meanings.
I don't think they would use Apocalypse for one of two main reasons: the first being that people would almost automatically think of it being "the Mortal Kombat to end all Mortal Kombats" and thus being something of a final game; the second being that there would probably be conflicts with the popular X-Men character and Marvel villain that bears the same name (X-Men Legends 2: Rise of Apocalypse is a just newly-released game, too)..