The linux version of the game requires the following libraries to be installed, they can likely be found on most distro repositories.
If you want to use the 32-bit version on a 64-bit OS, you will need to make sure to setup multiarch and install the 32-bit libraries instead.

I can't guarantee they will work on your system unfortunately, but the source code is publically available at https://git.magicalgirl.moe/KartKrew/Kart-Public and you can find instructions to help with compiling at http://wiki.srb2.org/wiki/Source_code_compiling

libpng
zlib1g
libsdl2
libsdl2
libgme
