Sure, pvp exists. It's not the most popular mode (co-op is the default and most popular way to play), but there is full support for this kind of scenario or mod: each object in the game is of a 'force' and you can't do things like open chests or mine (pick up) objects belonging to other forces (enemies). That's also how biters and player-built objects work. There is even a pvp scenario built into the game if I'm not mistaken and setting up a server is very easy (either with the in-game GUI or, if that's more your thing, with the dedicated server on Linux).
