Similar to Haaland, he also struggles against a back 3, remember Haaland didn't score against Bournemouth.
Unfortunately Haaland tends to have CBs completely gravitate towards him leaving space for others, and Alvarez doesn't quite have that gravitational pull, and/or the others didn't really make use of space provided as much as they could.
Not really a game I'd judge him on, I don't really see his future as a full 9 anyways.
If the intention in this game was to have him as a false 9, well that doesn't really work with Grealish and Bernie who are control wingers, false 9s needs fast wingers to make runs behind otherwise its a useless tactic. It's also completely pointless when a team sits back because we don't need more numbers in midfield.
He seems best when playing off of an actual striker where he can then find space better, in terms of his future role.
Aguero is obviously the greatest striker we ever had, and was amazing as a lone striker, but I always felt you saw his full arsenal when he was paired with another striker like Dzeko. Alvarez is similar to that for me.
Whether that benefits the other striker (Haaland or Dzeko) to their max strengths, I'm not sure.