Now I'm a bit confused how to use this environment. Especially I'm confused about how to tell GCC to build m68k-mint binaries and to use the mintlib, ... instead of it's usual Linux environment. I assume I need to set some environment variables like PATH and LD_LIBRARY_PATH to make sure make uses the cross compile environment.
It's quite easy. Sure, you need to point PATH (maybe LD_LIBRARY_PATH, too) to the folder where "m68k-atari-mint-gcc" is. (LD_LIBRARY_PATH, if needed, points then to that_folder_with_m68kgcc/../lib) . Mintlib & stuff is part of the repository, just install it, too. And then you try m68k-atari-mint-gcc hello_world.c hello_word.tos. And you have "hello_world.tos" Atari binary!