Those pre-built binaries are often targeted at more mainstream Linux distributions like Debian, Ubuntu, etc.
I guess it's possible to get SteamCMD running on Tinycore, maybe by providing certain versions of libraries (LD_LIBRARY_PATH=./libs) that are required from said Distros, but it's probably easier to just use a lean Debian based distro if you want it to just work.
However, I sometimes use libs from a Debian installation to get stuff working on Tinycore for personal use.