ITUNESHDVIDEO is described as boolean - which is probably not true any more. And the 0 should be treated just like the other iTunes proprietary fields.
For iTUNESGAPLESS you get the description
"Syntax: Set value to 1 or delete the field."
The same applies to
Syntax: Either enter the value 1 or delete the field"
For boolean values you can generally claim that any value that is not 0 is treated as true.
So entering 0 for ITUNESHDVIDEO creates a statement that "this is no HD video" - which is probably true for most files in a library. So to save space, the 0-value is not stored.
And again: even though MP3tag can create a non-standard field or atom, it is not responsible what the target application makes of it. The advice "Syntax: Set value to 1 or delete the field." indicates that other values are possible but that they are possibly invalid syntax.
If you do not follow the syntax rules, you will not get the desired results.