I have reviewed your arguments and I could make a substitution wording that instead of “general air superiority: and have it replaced by “multi role” and would still fit within the arguments that you have provided.
The legitimacy of your preferred description is predicated on the evidence that you can provide in direct support of air superiority and not by any critical evaluation of how others have got it wrong with their description. “Air superiority’ carries the function of air dominance whether in BVR or WVR i.e. it is an “Alpha” platform.
It is my opinion that your description needs to satisfy two tests i.e. the design test and the performance metrics test.
An airframe doesn’t become air superiority by accident but by design and that include trade-offs and optimisation of certain performance at the expense of others not critical to air superiority. The question therefore is whether you can provide any evidence in support of the fact that the J-20 was conceived as an air superiority platform from design. The AVIC poster in my view is more of an advertising description then a design description.
Aerodynamic performance especially air superiority function and stealth properties are not necessarily compatible and the reason why the F-117 ended up with the “Wobbly Goblin” description. That said, an “Alpha” platform is designed to go into a dogfight to prevail and that means it has to have the performance metrics to match its intended primary function. I am not a fan of aerodynamics but in a dogfight it is common to note two key metrics, instantaneous and more importantly sustained turn rates. The question is, does the J-20 have those kind of performance measures to qualify it as an air superiority fighter viz a viz similarly class air superiority fighters? The F-35 which is a multi-role fighter has often been criticised (incorrectly) as a fighter that cannot dogfight but to my knowledge it can execute a 28 degree sustained pedal turn, a feat that I believe very few other fighters can match.
The overall body of my thesis has been available in various forms for a while now, the most recent of which I have published here:
The summation of different indicators over time act together for why I base my position as where it is, with the main indicators including:
-J-20 pilot and test pilot testimonies regarding its maneuvrability
-AVIC's official brochure from last year
-Dr Song's paper
Supplementary indicators which are more peripheral/complementary to the main indicators include:
-Rumours about J-XX's role back in the mid 2000s consistently stating its role was to be that of an air superiority fighter.
-The doctrinal logic of seeking an aircraft for the air superiority mission first, before seeking other roles and missions that require the the ability to achieve/contest air superiority to be able to conduct.
The above points together form the basis my position which I think is an accurate reflection of the summation of relevant information WRT J-20's role to the best of our knowledge at present.
Edit: I have no issue if you wanted to call J-20 a multirole fighter aircraft either. There are few modern aircraft in the world which are single role.