Basically KPop is a genre of music which originates from Korea but are palatable to foreigners, and Paul Kim's music is not that.
KPop stan might have a vague definition but it is clear what is Kpop and what is not; if the genre of music is such that foreigners won't pay attention it is not KPop.
Sometimes, Gangnam Style or BbiBbi, while not produced to be Kpop, gained following among ifans so they are considered to be Kpop. (BBiBBi is still in the top 100 most viewed "KPop"Video and the only one not exactly Kpop)
IU began to produce songs which are more friendly to ifans so her journey remains to be seen.
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"pop" itself is not considered an artistic genre, but rather an amalgamation of other defined genre that is commercially "popular" at any point in time - hence "pop"
And what is presented as 'Kpop' does not originate in Korea, but has been mastered by Korean artists.
There is simply no clear definition for it, it terms of beat patter, notes, signature chord progressions or unique set of song structures.
So it is entirely perception and only applicable if the artist/song itself is not clearly tied to a genre like hip-hop, rock, jazz, R&B etc.
After all while everyone and their halmeoni, thinks IU was always a part and leading light of Kpop, while you constantly excluded her until Bbibi is it?
You definition of Kpop seems to depend on popularity with ifans, which is a fallacy.
So unless Paul Kim explicitly is tied to trot or gugak etc., given his popularity, his music ought to be Kpop, never mind if he is unknown to ifans.
I think a better definition of Kpop would,
#1. Popular music produced in S.Korea
#2. By acts created/associated to the idol-trainee system
Which makes IU always Kpop and Paul Kim not Kpop.
There is no distinctive sound to Kpop otherwise to claim it as a genre. It is a commercial entity which sells art and not artistic entity like Blues, R&B, Pansori etc.
It is like Hollywood - which is not same as movie genres like Horror, Comedy, noir, Romcom etc. or acting methods.