I have multiple of what I'm very confident are basically those devices. I use them fairly regularly.
They are almost all built around the MS 2109 Macrosilicon chip (and the ones that aren't are worse). They will only do MJPEG when above a certain rez and framerate.
1080p60 24-bit colour depth is 372.5MBytes/sec uncompressed. So it's going to require some compression.
I'm not an expert on h.264 etc, but can you do real-time lossless CBR below 53MBytes/sec on a readily available hardware encoder that, including the HDMI capture functionality, comes anywhere near $8?
Yes, for anything higher quality (UHD 4K) you need more expensive hardware.