The game does work in the itch.io client btw, but you'll need to Install it first. And then you can play offline :)
Viewing post in Dicey Dungeons v0.10.1 (Bugfix update) comments
Oh, must be that v23 (current stable) bug about spaces in file names for HTML5 games.
I've been playing it in the v25 beta, works great there :)