That is what I thought. I just tried and downloaded both versions a second time. And as before, I can launch 4.13.0 but 4.13.1 results in the above error message.
I just had a look at https://distrowatch.com/table.php?distribution=mint
Linux Mint 20.3 uses a newer glibc 2.31, my current Mint 19.3 is using glibc 2.27. Not sure if that matters though, as I thought the AppImage would take care of that. Unfortunately, I can't risk switching to Mint 20.3 right now.