With the term "HDR", they have actually bundled together two improvements. Not just higher contrast, but also wider colour gamut.
HDR and UHD BluRays are encoded with Rec. 2020/Rec. 2100 colour spaces. These are wider apart than what any camera is capable of, just to be future-compatible.
BTW. Theatre projectors use DLP with a rotating colour filter or lamps or lasers in primary colours, not LCD with just a white bulb like in most home-projectors. These have a contrast ratio of at least 1500:1.