I was about to object, but actually it looks like you're right; tigcc appears to only target the TI-89 et al. which run on the 16-bit Motorola 68000 series. A quick search doesn't give me any C compiler for the TI-84 after all.
Your actual point, of course, is valid regardless:)
EDIT: Oops, actually https://en.wikipedia.org/wiki/Small_Device_C_Compiler ... but then you're right about getting pretty obscure.