EDIT: Looks like it's essentially a demo. It's a limited, non-fully-featured version of the game.
I believe its just the 'battle royale' component...
Yes, but it seems even that is limited (emphasis added below):
The [complete edition] includes extra game modes, cosmetics, online co-op, and a full singleplayer campaign
So from the sounds of it, you can play online free-for-all PVP but you can't play online with any friends/team-mates.