The listed photos are just at the wrong angle to be able to read the chip markings (grr)... but I had a bit of a further poke around, and found a listing for a discontinued internal board for HTPC (!) setups: https://www.pulse-eight.com/p/117/internal-hdmi-cec-adapter
A reasonable bit of eye-strain later I at last identified that I was staring at an AT90USB162-15AU. Here's a reference for the -16AU: https://www.mouser.com/ProductDetail/Microchip-Technology-At...
Huh. 16MHz. That answers that then.
(Now I'm a tad more idly curious why the firmware was unreadable.)
Otherwise you might try binwalk with the --disasm option (you'll need capstone installed for it to work) then it will attempt to search files for assembly for any of wide range of processors (obviously would fail if the firmware is encrypted, but I doubt a cheap product like this would bother). I'll also just briefly say that even though RCDATA is microsoft's recommended way to embed a file into an executable I've seen plenty of software that embeds files in other creative ways, so I wouldn't rule out the possibility that the firmware is somewhere else in the executable, binwalks entropy analysis mode can sometimes work firmware that is otherwise hard to locate.
1: https://www.pulse-eight.com/p/154/intel-nuc-hdmi-cec-adapter