That’s it — doing that ‘secret’ puzzle counts as playing a game, apparently. Not 100% sure that it’s a ‘bug’, but definitely not something I’d expect.
Not a bug, working as intended
As far as I can remember, “play a game” has always counted any game mode, including PVE
I’m not so sure about it, although I don’t remember for certain. I don’t think PvE content like bounties used to complete the ‘Call of the Brawl’ quest, for example, but I might be mistaken — it’s been a while.