I wanted to reply with a bunch of DSP examples but on further investigation the ones I checked just now seem to very deliberately use the term "data word". That said, the C char type in these cases is one "data word" as opposed to 8 bits; I feel like that ought to count as a non-8-bit byte regardless of the terminology in the docs.

NXP makes a number of audio DSPs with a native 24 bit width.

Microchip still ships chips in the PIC family with instructions of various widths including 12 and 14 bit however I believe the data memory on those chips is either 8 or 16 bit. I have no idea how to classify a machine where the instruction and data memory widths don't match.

Unlike POSIX, C merely requires that char be at least 8 bits wide. Although I assume lots of real world code would break if challenged on that particular detail.