I think it is self-evident that contemporary distinctions between frigates, destroyers, and cruisers, are so muddled as to be confusing or misleading, rather than a source of conceptual clarity which is the entire point of having such distinctions in the first place. Such confusion is predictable because it reflects not only differing usage of the terms by various nations, but evolution of warship designs over time. Any conceptual hierarchy is necessarily the product of a particular place and time and is intended to serve particular purposes (i.e. chiefly to describe one's own navy, and those of the most relevant foreign nations), and we should anticipate that it will become less coherent and less useful as distance from those "elements of origination" increases.
The question of whether 055 is a destroyer or a cruiser is, to my mind, basically two questions: the first is how PLAN officially characterises the ship. Such official classification is not necessarily authoritative for the rest of us, but I think it should enjoy a certain degree of privilege. That is to say, we should use the official term unless the use of that term is more confusing than revealing. For an example of where national privilege should prevail, I would point to the Horizon-class frigate. It could conceivably be labelled as a destroyer, but France calls it a frigate, and there is no compelling reason to override their classification. For an example of where external classification does/should prevail, I would point to the Hyuga and Izumo class "destroyers". Japan's classification should be acknowledged, but in a broader global context the vessels are quite different in function, layout, and appearance to what we usually think of as a destroyer. Thus, it makes sense for us to refer to them as "ASW helicopter carriers", whilst also acknowledging the Japanese classification.
Besides official classification and the privilege it should be granted, I think the question of whether it makes sense for us to refer to 055 as a destroyer or a cruiser fundamentally reduces down to how we think of the type in the context of the Navy. Because I view this ship as a successor to the 052x series, not a complement to it, I favour the classification of destroyer. For those who see PLAN producing both 055 and smaller, 052x destroyers alongside one another into the indefinite future, it makes sense to distinguish the former from the latter by labelling it a cruiser, in line with its greater size. Such produces a neat scheme whereby PLAN produces one corvette class*, one frigate class, one destroyer class and one cruiser class. There is an appealing unity and correspondence between class, displacement, and classification. But that is true only if the 052 series does indeed have a future, of which I am far from convinced.
* And of course we have already confronted this question with 056. So far as I can tell, PLAN classifies this ship as a frigate. "We", on the other hand, have apparently decided to label it a corvette, distinguishing it from the much larger 054 class of frigates and better contextualising it in the context of western frigate classes.