You're right, if you're not selling the game here, then the Itch.io page is only for marketing. Even if it doesn't appear in searches, you can still post devlogs, release announcements and so on. People can put your games in collections, and it will be recommended to others.
It's curious however that the app store link doesn't show a nice big button like it should. Are you sure you're putting the link in the right place? It looks as if you just duplicated the link in metadata.