PvP means player vs player right? What about coop multiplayer games where the goal is to work with other people? Do those fall under PvP based games?

Nope, this isn't PvP, and there is no rule against that. There is a reason why the site supports multi-player runs.

Purely co-op games are extremely rare, but https://www.speedrun.com/a_way_out comes to mind. I'm sure there are a few out there, and yeah, they're fine.

PvP really stands for player vs player but it could also stand for players vs players. Resident evil 5 and 6 are co-op games for example. But.. I think what you are getting at are games like Project Resistance but I don't know if you would officially classify that as PvP because technically you are working together as a group to meet a goal/objective even there besides the co op element there is another player playing as a mastermind where they setup obstacles in your way such as tyrants and other enemy AI. I didn't check to see if games like that were added to the site but it would seem to be co op. Think Left 4 Dead except replace the AI director with a human director. Hope this helps but I may be wrong about that game and it could technically be classified as PvP. There are games that have PvP modes that also have pure co-op campaigns that are allowed like RE6 and Aliens Colonial Marines for example. I could name them all day but you get the point. Hope this helps. :)