Regardless of how much combat, exploration, or social aspects your game has, your game should have shenanigans as well. In that light, as they are a requirement of the game to run well, they are a pillar of the game. There are multiple features in the game, such as ribbon class features and a number of wacky spells and magic items, that exist purely to have fun. The common magic helm that gives you red eyes or the cape that always billows has nothing to do with combat, exploration, or social, but its a really fun thing to have, so it falls under the shenanigans pillar. Rigging a acme-esque trap to do some nonsense thing to trip up enemies chasing you doesn't really feel like combat, exploration, or social either, but is a shenanigan I'd expect to have in a game.
So, its a real pillar.