can you play multiplayer on it, whether on the same PC or via internet? Like, could I buy 2 copies for my wife and my computer and play each other?
You can play it on any 2 computers as long as you have two steam accounts. If you also have the version on iPad, you should be able to play it against someone who is playing on a PC.
"When playing Online, you are connected to the same servers as the players of our Web and iPad versions, in addition to the PC and Mac."