What's the current method to get the game to start on Big Sur? Neither starting the jar nor the Mac executable work. 

First you need to 'chmod 755' the executable file.  

Then, you need to download new Java Runtime Development (https://www.oracle.com/pl/java/technologies/javase-jre8-downloads.html)

Then you need the following steps:

1. TalesofAndrogyny.app (or whatever its name is), show the contents of the package and in the Contents/Resources folder either remove or change name of the jre folder

2. Unpack the JRE.tar file (again don't remember actual name my recent one was: jre-8u301-macosx-x64.tar) and copy the Contents/Home folder into the Contents/Resources folder of game package. Then change its name from Home to jre.

This worked in my case.