The short explanation
Hybrid Log-Gamma was developed by the BBC and NHK for broadcast. Its trick is that a single signal works on both kinds of display: an SDR screen sees a normal picture, an HDR screen sees the extended range. No metadata is required, which is what makes it practical for live transmission.
Where you run into it
If you watch broadcast sport or live events in HDR, HLG is what you are receiving. It is not used for discs or most streaming films, so its absence in one place and presence in another is normal rather than a fault.
Like every HDR format it has to be advertised. A chain that lists HDR10 but not HLG will simply not carry broadcast HDR through, and the result is a correct-looking SDR picture that gives no clue anything was lost.
How the DR HDMI 8K handles it
The DR HDMI 8K's HDR flag includes the combinations that matter here: HDR10 with HLG, and HDR10+ with HLG. If your broadcast source is not offering HDR, checking whether HLG is being advertised is a good first move.
Want to test your own HDMI chain?
The DR HDMI 8K is sold through the HDFury.eu web shop.