It's unlikely to be high video quality though, as all of the similar HDMI capture devices that I have (~7, known as the "Can'tLink" devices as a play on "CamLink") will only do decent framerate at reasonable resolutions in MJPEG.
Quick Edit: Also, if you get one, check there's a tiny heatsink on the chip inside otherwise they cook themselves.
I'd start by looking at the Black Magic Intensity Pro 4K, but you're looking at hundreds of dollars.
Yes, for anything higher quality (UHD 4K) you need more expensive hardware.
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?