The problem is that Itch is DRM-free oriented and has no activation mechanism.
When a game needs activation, it's because the game's developer has implemented this system. To receive help, it's best to try contacting the game's developer directly, looking for a contact email in their profile or writing directly to the page where you purchased the game (at the bottom of the page).
If you can't reach them or want to escalate the issue and request a refund, it's best to contact Itch support directly. But remember, since activation is implemented by the game's developer, support won't be able to help you activate it. At most, they can help you contact the developer or refund your money, since you can't play.