Thanks for the comment about the game. If you are enjoying it, it's a tribute to Linda.
Thanks for the link, but the game already deals with orientation perfectly. The bug occurs in the Itch wrapper around my HTML5 game, therefore there is nothing I can do, as orientation information seems to be intercepted and withheld from my application.
I have posted the bug report, and I'm sure that it will be resolved soon enough.
The Beast is the first HTML5 application of this genre that specifically targets mobile (I believe), and it really has been designed to REQUIRE portrait mode (on tablet, it is much less of an issue due to more screen space). These teething issues will pass.