These chips use the rather obscure Xtensa instruction set. While a port of GCC exists and Espressif provides precompiled GNU toolchains, there is no support yet in LLVM (although there have been multiple attempts.
There are two ways these chips might be supported in the future, and both will take a considerable amount of work:
The compiled LLVM IR can be converted into (ugly) C and then be compiled with a supported C compiler (like GCC for Xtensa). This has been done before so should be doable.
One of the work-in-progress LLVM backends can be worked on to get it in a usable state. If this is finished, a true TinyGo port is possible.