Hi,
I've been using this reddit guide explaining how to install the itch.io Windows launcher on Linux, and it's been working well for me for Dog x Bloods. If that can help someone else:
https://www.reddit.com/r/SteamDeck/comments/vwili3/better_way_to_itchio_on_steam...

A few things: 

• Follow every steps in "How to do it?"
• Once you downloaded the game, it took me some time to launch it (1-2min) but it will launch

If someone needs help, I would glad to try to help.