No, it isn't. Absolute luminance is a "feature" of PQ specifically used by HDR10(+) and most DolbyVision content (notably the DolbyVision as produced by an iPhone is not PQ, it's not "real" DolbyVision). But this is not the only form of HDR and it's not even the common form for phone cameras. HLG is a lot more popular for cameras and it is not in absolute luminance. The gainmap-based approach that Google, Apple, and Adobe are all using is also very much not absolute luminance, either. In fact that flips it entirely and it's SDR relative instead, which is a much better approach to HDR than what video initially went with.

Ideally in the abstract it could be just that, but in practice it's an umbrella name for many different techniques that provide some aspect of that goal.

Not in the more general sense! It can refer to what its acronym spells out directly: Bigger range between dimmest and brightest capabilities of a display, imaging technique etc.