Hello,
Thanks for asking! The primary accessibility feature is screen reader support - the game is built with web tech, so it works very much like a browser. I don't have the expertise or resources to say much about the experience myself, but I've had some direct feedback from the AppleVis community using VoiceOver on the iOS version, and after some fixes at their suggestion, they seem quite pleased.
The game is entirely text-based (other than a handful of illustrations for flavor), so screen reader users can experience it in its entirety. It should also be fully playable with a keyboard, though it was designed for mouse or touchscreen first.
Controller support, on the other hand, is not something I've specifically implemented or tested for. I would assume it won't work, though I don't actually know either way.