"Stygiansilence: The event page is failing to recognize that some people downloaded TF2. If you're having issues, people on Discord are saying to play an hour of the game. That way it'll recognize the game as owned."
Thank you, I can confirm that this worked (after 2h, in my case, as I forgot to check it earlier).
Also, deactivate uBlock and Privacy Badger, if you have them, in the TF2 event page of Alienware too, otherwise the "Join" button won`t work.