You can't play the campaign in co-op.
But you can compete in 'Deathmatch' or 'Collect the Flag' modes for 2-8 players.
I haven't tried that yet, though.
Can someone who purchased the game confirm please what exactly the "Online Co-Op" tag on Steam means in practice? I don't suppose it means that you can play through the campaign with one buddy, rather the other multiplayer game modes, but it would be nice to know. Thank you.
I can confirm that's likely a mistake, the MP modes are just the competitive ones from the original game.