Then again, one could always note that per EGG, the only way to gain XP from monsters was if you killed them. Not if you tricked, charmed, snuck past, or otherwise defeated them - killing them. Heck, you didn't even get XP for "defeating" a trap - traps and puzzles were just ways of whittling down the characters' resources (Tomb of Horrors notwithstanding).
I would argue that originally D&D was conceived as a combat-focused game with elements of roleplaying, exploration, and the other things people have mentioned. In effect, all those other rules were mostly to help you get...into combat. There's a reason why many people equate D&D with "killing things and taking their stuff".
Is that all D&D can be? Of course not. Is it all D&D is to most players today? I doubt it. Is there any other single element that is more common in D&D games? I doubt it.