MrMFS found the solution but it's not working fully.
Game pages woks differently (example. Game dismantled. URL starts like this bigprojectalone.itch.io) because of the custom link name, hosts stops working and again we are having "error_connection_refused". If i'm gonna add this to hosts "173.255.209.84 bigprojectalone.itch.io" it suddenly working again.
The problem is... Everyone's pages is named differently... so you have to manually add them into hosts if you wanna have access to the site.
When I opened forbidden game page, I got PR_CONNECT_RESET_ERROR
From this I can assume, that the blocking works as it should (only for one page)
Hopefully, the problem is on itch.io side, and the website will be fixed soon.