Does HDCD give you more fidelity?

The old format HDCD brings 20 bit into your living room. The extra bit depth you get instead of the standard 16 bit that CD have. Results in a greater dynamic range (theoretical 24db more).

But you do not use the whole dynamic range anyway on a disc anyway. So 95% of the time when the use 24 bit like on Blu-ray Audio discs it doesn't mean that the recording utilities all the dynamic range that is possible to use for the format. So it is misleading.
So in the final end for example a HDCD can have more dynamic range than a blue-ray audio or SACD. Because of how the content has been handled before ending up in the disc.

But in HDCD they often (but not always) set something called "peak extend" option in the encoder during the encoding to digital (AD Conversion).

The requirement is too get the benefits you need a player or software that can decode HDCD otherwise a it will be played as a standard CD and there may not be any benefit to the sound quality.

For the ADC use Pacific Microsonics AD converter that some says that it is one of the better sounding AD converters out there even today. (custom dithering, audio filters, and some reversible amplitude and gain encoding) The Pacific Microsonics is able to do that nice audiophile style dimensional sonic image.

The disc on the video are:
Dire Straits ‎– Sultans Of Swing (The Very Best Of Dire Straits)
Label: Vertigo ‎– 558 658-2

That you maybe can find a second hand copy here:
https://www.discogs.com/Dire-Straits-...

What I notice when playing this disc is the higher dynamic range. Not only do I hear it it also shows on my equipment in the form that I need to turn up the volume control much more to reach my normal listening levels.

That's a tell that the disc may have more dynamics than other discs.
The teoretical is that you have max record level that is the roof. If you want to extend the dynamic range than you can only extend it by make the floor going lower. The result is that the median level is also lowered. So if then want to play that disc at the same listening level with more dynamic range then you need to crank up the volume.

The result is that you get lower lows and higher high levels. So in this case for example in track five "Private Investigations" in the end of it (and other tracks) you will get sudden drum strikes that comes from nowhere and with breathtaking intensity..
I just described what higher dynamic range will do for you.

I have bought an old oppo (bdo-83) that plays all of the formats mentioned here and even several others. And it is highly recommend.