Wow that's pretty ancient as far as forum software goes, amazed it's still running!
Looking over those wayback machine links, seems it's built on Perl and, in the professional version at least, a MySQL database. If they are using MySQL, that might mean there is some hope for migrating it to a new platform as the vast majority of forum software still uses MySQL as their database. That said, they're going to need to write a custom importer and/or a variety of scripts to move that data over. Even more so if they want to keep accounts and user data. That said, since it looks like DiscusWare doesn't actually have that many features compared to modern software, it certainly won't be an impossible task.
I'm sure they've already got options in mind, but here we've been very happy with XenForo 2 since we moved away from vBulletin at the start of last year. It's been very stable and regularly updated (and updates are easy to install). It does come at a cost (initial purchase and then yearly update fee), but for us at least it's well worth it. For free options, PHPBB and MyBB are the two big options in the open-source world, and they're both very good (especially for free!).
