[I don't remember whether there are any other extra requirements/what happens at display scan out, would need to check DVI/HDMI/DP spec &/| Windows too...)
I believe so. There haven't been HDR monitors (and still aren't) so there's no way to display a 10 bit output. There may be displays that take a 10 bit input and tone-map them themselves(?). HDR is a New Thing requiring an HDR display to work, and these are presently only 4K TVs.