It's a fun comparison, but with the notable difference that that one can compile the Linux kernel and generate code for multiple different architectures, while this one can only compile a small proportion of valid C. It's a great project, but it's not so much a C compiler, as a compiler for a subset of C that allows all programs this compiler can compile to also be compiled by an actual C compiler, but not vice versa.
But can it compile "Hello, World" example from its own README.md?
https://github.com/anthropics/claudes-c-compiler/issues/1