According to Wikipedia Mint was released in January 2024 and is supported until April 2027. That isn't old.
That's not really the issue (and it's good it still gets updates for two more years). JRiver only officially supports Debian and it was announced a month ago that MC34 would be moving to Debian Bookworm as the base/build system. The issue here is Linux Mint 21.3 (and likely Ubuntu 22.04 LTS too) are older than Debian Bookworm and ship with libraries and dependencies, specifically glibc, which are too old for MC34 to run correctly on it. The distro you're using either has to match or exceed the version of the library/dependency (glibc in this case) for MC34 to function correctly. Yes, Bob and the team does sometimes address issues with getting Media Center running on non-Debian distros, it doesn't change the fact that a) they only officially support Debian and b) the distro you're using has to match or exceed the libraries/dependencies needed for Media Center to function correctly, otherwise it's too old and likely won't work. This is no different than macOS when new MC versions have to target a new minimum version of macOS, though in Linux it'll happen faster. System requirements change as time passes, the minimum version of an OS changes a specific version of an app runs on will change too. That's how it always has been with all OSes.
And as I said, Linux in general is the most unforgiving platform when it comes to maintaining backwards compatibility with newer apps and older distros that have older libraries and dependencies they ship with (especially glibc) becoming too old to run certain apps. Windows is the best platform when it comes to backwards compatibility, then macOS (though it's not great either honestly) and then Linux.