I haven't seen it myself, but I'd imagine it contains scenes portraying current 'senior royals', and other significant people such as political or media figures, having 'private' conversations about sensitive issues and no doubt part of the drama also involves the use of background music. Since several well known and recognisable actors are involved it seems unlikely that anyone watching would think that this wasn't a drama, and that the dialogue used and events portrayed were intended as accurate history.
I wonder if anyone was ever confused by, and having had a look at the cast list, Prince Philip being played by an incarnation of Dr Who: I suspect not, so maybe those who think it needs to be flagged as 'drama' are under-estimating the nous of viewers.