"Hypercompression", while a term used for quite a while in several different disciplines (if audiophilia is a discipline), has not been clearly defined, nor is it in common usage in the recording industry. Sure there are a bunch-o-Google hits, that just means people use the term, that doesn't mean it's universally used in the industry, nor defined at all. There are a lot of audiophile terms like that (do we need to go down the blurring path?).
Indeed, "compression" cannot be defined simply to the extent that "more" or "less" has any meaning without understanding many more parameters such as independent attack and release times, threshold, detector characteristic (average, peak, RMS), ratio, as well as the obvious degree of gain change. It is possible, for example, for a compressor to operate 20dB above threshold, and by simple parameter change be heard as "more" or "less". It's also common to apply compression at the track level, which completely changes the concepts of "more" and "less". Compression (and limiting) are also sometimes applied by splitting the spectrum into semi-independent frequency bands, further changing what "more" vs "less" means in the result. It would be incorrect to assume that, for example, 4 bands of compression followed by 4 bands of limiting would be default be "hypercompression". With the right parameters, it could sound almost unprocessed.
Hypercompression implies "more" of something that has not been defined other than general "compression", and "clipping". If you include "limiting" (a somewhat more defined case of compression, but only somewhat), the definition blurs even more. All we can assume is that "hypercompression" is, at least to some, an objectionable amount of program-based automatic gain change. But then, "objectionable" is a subjective term, meaning it is determined by opinion and not measurement. So we don't really have a handle on what hypercompression is, even though the term is used here and there.
The 2014 AES paper
"Hyper-compression in Music Production: Listener Preferences on Dynamic Range Reduction." - (Robert W. Taylor and William L. Martens) bats the term around freely without defining it other than to document the particular compressor and settings chosen for their paper. The paper attempts to determine listeners awareness of hypercompression in various genres, then determine preference. What's interesting is their results, which show a remarkably uncorrelated preference in most genres tested, with classical being the stand-out that did have general agreement that little or no "hypercompression" was desired. The other interesting possible correlation was not fully explored, that of influence of the cultural and creative models of the individual genres of music used for testing. However, the paper suffers from a limited definition of hypercompression, a limited number of samples, and, relative the the recording industry in general, a severely limited selection of the types of compression.
It seems silly to have to point this out at this late stage in the...um...conversation, but compression, limiting, and clipping are all fairly different things. Each can be used inaudibly, to audible benefit, or to excess with subjective benefit or detriment depending on who's listening. Further, when peeping at a music waveform in an editor, the flat-topping is not necessarily clipping, limiting looks quite similar until you zoom into the single wave level. Clipping, if it actually does occur, is not always audible. The audibility of hard clipping depends on a complex combination of time, frequency, degree, and total active spectrum which is quite capable of masking clipping induced distortion products. Clipping audibility covers the full range from completely inaudible to gross distortion, but to assume that just because something looks clipped that it is, and that clipping is audible at all would be naive.
If excessive distortion is heard in a recording, we could put part of the blame on intersample overs, which have the ability to push some DACs into hard clipping even though no samples go above 0dBFS. Benchmark provides
this info. Who is to blame, the DAC, the mastering job, loudness war? All of the above? Sure. And that specific issue can be solved by any of the three. One of those resides in the realm of the audiophile!