I think his transfer market in general is locked not just the web app one, which i think is the one you unlock by playing more games, going by his screen shots, 178+ hours of game play + hes done the objectives it tells him to on that error dialog so something does seem off, my transfer market was unlocked 1st day playing for me (on the game not web app)
only thing I can think is to contact EA Support / Live Chat as it does look bugged, you have done what its asked you to, nobody usually has issues accessing that transfer market