Itch.io does not provide an account system.
Quite annoying since i do not want to play using the steam client.
Is there any solution for this kind of situation?
Refund and buy the game on Epic instead, or play the mobile version for free. The itch.io version of the game doesn't have proper support and the devs aren't taking it down in spite of not being a competent version of the game. They said they were going to look into fixing it but have published a roadmap since that statement with no mention of the problem being any kind of consideration any more, and no solution has been provided since.