The problem you’re having is the same as on this thread:
The short summary is that from 3.7.10 onwards, the version of Java we bundle in our Mac release package won’t work on very old versions of MacOS.
You can still run the “other” package of Vassal on your version of MacOS, and we’d very much like to work out exactly how, but we need somebody with such a Mac to help us work through it or it won’t happen. Follow that thread to the end, working through the steps and report back there what you find.