Dont you think it is an issue with your phone? I tried it myself after reading your post and it does not go to landscape once I set my auto rotate off. It must be an issue with your phone or browser imho, is it happening when you open any other websites on your browser?
Mine also works as intended, no auto-rotate stuff.
@Text you should restart your phone if you have a problem with auto-rotate. Sometimes mine stuck like yours, but it will behave correctly after a restart.
Other than that, it might be a problem with your browser or browser settings.