"An abstract strategy game is a strategy game that minimizes luck and does not rely on a theme. Almost all abstract strategy games will conform to the strictest definition of: a gameboard, card, or tile game in which there is no hidden information, no non-deterministic elements (such as shuffled cards or dice rolls), and (usually) two players or teams taking a finite number of alternating turns."
What you'll notice here is that definition above has two separate elements: deterministic play, and a lack of theme.
But if we look at a definition of the phrase abstract we find "existing in thought or as an idea but not having a physical or concrete existence.". Which you'll notice only seems to be a match with the second element of our definition of abstract games (which I think we can concede is equivocal with an abstract strategy game); the depth of strategy is not implied by the word abstract, although if we acknowledge that abstract is in fact shorthand for "abstract strategy" this disconnect is somewhat solved, even if it feels a little lazy.
So, what we can see, is that at some level, stereotypical abstract games, such as Go, Checkers, Pachisi, or Backgammon all lack any real theme, they are games about abstract concepts, they lack any tie to physical form. If we think about the word abstract within the context of its usage as a verb, we can even begin to semantically justify the fact that games WITH themes are in fact abstractions of real things; they are crude simulations. But I digress I think we shouldn't jump ahead quite yet.
What seems to have happened, and early enough that it really predates the modern hobby scene, is that the common trait of fairly strategic/deterministic play in many early games which have persisted to the modern day, and many of those games are either purely abstract, or are abstracted in a way that is not comparable to modern games (cf chess with Agricola). So, by extension, the notion of an abstract game, or really an abstract strategy game, became something that specifically had both terms as meaningful appelatives. But, because the phrase "abstract game" is usable both as a standalone term and as a shorthand for the more specific "abstract strategy game", you run into an issue in which defining whether something is or is not abstract depends on what you use TO define it, and this becomes an issue when there is no shared consensus.
Is the game Patchwork abstract? It is certainly a distant abstraction from quilting actually is, but it still has a viscerally visible them; At the same time it is pure fixed information, the layout may change but the information is all available. So if we are looking at the term abstract as referring to both the distancing from a theme, and the non-literal representation of an idea (so both the adjective and verbal concepts), AND the shorthand for abstract strategy, suddenly the definition is so broad as to be meaningless. We can certain agree that some games are themeless, and some games are very deterministic, and some games are both, and certainly there are games that are neither, but the vague, nebulous term "abstract game" seems to be overly broad, as it really only excludes games that share neither of the central elements.
So, really, the key takeaway seems to be that the word abstract, when describing games, does not necessarily share the same meaning as when it is used in the term abstract game. If we're just using words as isolated units within a grammatical construct, then we can recognize that a game can be abstract, or have strategy, or some combination, but the semantic confusion arises when we start to use words in a non literal sense, and in fact, frustratingly enough, abstract the meaning of the word abstract itself from its literal meaning, and create this very strange scenario where a term consisting of one adjective describing a game may in fact be representing any combination of two entirely distinct adjectives.
This is how language works, and it's frustrating, but evaluating it, and using it to further inform how we approach both language and the meaning of that language is what becomes impotrtant.
Is Hive an abstract game? It's like Chess, but is that abstract? It's certainly an abstraction, in one case of insects.. moving around, and the other of various elements of a medieval heirarchy in pseudo war. But the answer to the question "Are these abstract strategy games or simply strategy games, or abstract games" is a confounding "Yes".