No.
You don't understand HDR. It's not about color gamut. You can buy a projector with 4K resolution that accepts and projects HDR, even though it is not capable of covering more than REC.709.
Is that HDR? Yes. Is a 1080p that accepts a 4K HDR signal but is limited to 1080p, does it display HDR? Yes
Does it meet all the specifications? No.
But many displays, TV or projector, can't either. Projectors can't reach the kind of nits a TV is capable of, and even if it could, the size of regular screens would make it too bright.
A 65" TV at 1000 nits is very different from 120" screen at 1000 nits.
HDR on projectors is an adaptation, not what the standard was meant for, which is TVs.