Thanks a lot for the kind words and the re-purchase! I'm really happy that you like BOH to the point of returning to it even after so many years - and buying it again, even! I hope you'll manage to enjoy the latest version, which, being the result of 10 years of free updates, is much better and richer than the 2009 edition.
Regarding the technical problem: BOH is a 32-bit application and, as far as I know, Apple dropped 32-bit applications support with MacOS 10.15 (see here); I guess that it's what the issue boils down to. Unfortunately, I can't afford to support also platforms that break compatibility (on top of that, after those 10 years of continued development, BOH is now really a closed project). Maybe there's a way to run old applications (I'm not a MacOS user, so I don't know)? Like, for example, DOSBox to run MS-DOS applications on modern Windows systems.
Out of curiosity: given that you had already bought the game, you were entitled to download it from here as well; didn't you get a key code with the original purchase?