It’s about sharp (Dictionary.com, Merriam Learners, Merriam-Webster, American Heritage Dictionary). Only Wiktionary mentions a chess context with the meaning “tactical; risky”. On Chess SE, the top voted question is about very aggressive [chess] openings: the person discusses an opening and says it “makes for a sharp tactical game” and requests further information about “very aggressive, tactical, sharp open games“. There are some 14 other instances of the adjective sharp being used in the answers and comments throughout that Q&A. One answer discusses another opening and says it’s “sharp, but sound and deep“, seemingly implying it’s possible to have a sharp yet unsound opening, and if it’s unsound to begin with then it that can’t be so keen in intellect or even that much tactical for that matter. Also if it means tactical then why would the person asking say “sharp tactical…”?
The notes about sharp, keen and acute in the AHDotEL are also very interesting:
Figuratively they indicate mental alertness and clarity of
comprehension. Sharp suggests quickness and astuteness. […] Keen
implies clear-headedness and acuity. […] Acute suggests penetrating
perception or discernment.
[ American Heritage Dictionary of the English language, sharp. ]
Especially since Merriam-Webster lists as second and third meaning for sharp many shades of keen in (…intellect, perception, attention, spirit). Merriam Learners is also interesting when they refer to “having or showing a quick ability to notice and understand things” with an example like sharp questions, which makes me think that the product of a sharp mind may be sharp too…
More broadly speaking, there are other phrases/adjectives such as cutting edge (technology), tip of the spear (?), state of the art (device?), contemporary (time based), or things like focused, precise, which I tend to associate one way or another with some of those many meanings sharp can have. More typically I’m used to sharp being used to mean clever or cunning to describe someone, especially when they say something sharp, and I wasn’t really aware this could be informal or that it could be used for stylish (informal) or expert (informal).
Is there a chess specific usage for sharp, what does it mean, is it “tactical; risky”, are those just different use cases from books separated by a semicolon; has the word sharp become more popular over time, along the lines of stylish/cool, or has it replaced bright for quick-witted/intelligent (Dictionary.com) in modern casual English i.e. is the chess usage adapted from general usage, or different from it; when it modifies other adjectives and qualifies inanimate things and abstractions, or figuratively, is sharp just an intensifier, like the adverb “very”, or do you pick up the nuances from context so that you feel it’s one of aggressive, complex, modern, vetted by pros, popular, or stylish, depending: which one was it in the chess question (sharp tactical game/very aggressive sharp open games)?
Sharp is an adjective. It has a particular meaning in chess, and you would need to be a chess player to fully appreciate its meaning (I’m not). Its meaning is hinted at by the use in the forum. A sharp game means that the player needs to think deeply about move sequences, and characterised by lots of exchanges of pieces, contrasted with a game in which a player is able to use patterns of pieces to choose the best move, and the position becomes blocked. The meaning is apparently an extended from the usual meanings of “Exact, sudden, cutting”. (“Exact” because any error would lead to a big loss, “sudden” because there might be sudden large exchanges of pieces, “cutting” because of the large loss of pieces on both sides.)
An opening may be sharp and unsound (aggressive, but a bad move, for example, bringing the queen out too early). It can also be both sharp and sound.
As for register, would be “technical” or “jargon”. This use is not part of most people’s vocabulary. You can’t generalise to use outside of chess. You can’t use sharp to mean “aggressive or risky” when talking about a business plan, for example.
As you note from the dictionary, sharp has a large number of secondary meanings. The chess meaning hasn’t made it into the other dictionaries, yet the forums show that it has currency in the chess sub-culture.