Though it's worth noting this is one file in one component. The kernel entry being C-free doesn't necessarily tell the whole story. If you peek at that directory listing in the blog post, relibc/ is in recipes/core. reblic is Redox's libc replacement, which is mostly Rust, but has historically needed a C compiler for some POSIX compatibility shims.
And the bootloader, firmware handoff, and build system are all separate questions.
So the short answer to the original question seems to be: the kernel itself bootstraps from minimal inline asm directly into Rust, no C in the path. The full OS build story is probably more nuanced than any single source file can confirm.