Unepic is a 32-bit application, apparently, so it does not run on macOS Catalina (Version 10.15). This was a known issue before the release of Catalina, but it's still disappointing to see it finally happen.

If anyone has a different experience and somehow gets it to run, please let us know. Otherwise, well, this is why I created a VM with macOS Mojave in order to run legacy apps.

EDIT: The store page was finally updated, so this post is now moot.