This is a standard problem that happens when visiting a Twine game hosted on itch.io with some sorts of cookies disabled in your browser (third-party, I think).
If you don't want to enable those cookies, you can work around it by opening the frame containing the game directly. For instance, in desktop Firefox, after dismissing the "no valid storage adapters found" pop-up, you can right-click on the game area, choose the "This Frame" submenu, and then "Open Frame in New Tab" (or one of the other options according to taste).
(Other game engines, such as Adventuron, also have the same underlying problem, with the same solution, but it manifests differently.)