Thinking it through, it's not very clear. But I think it leans towards Jhin possessing a little magic.
His hextech accelerator part of his gun is, clearly, hextech and thus magic. I know -somewhere-, It's simply described as enhancing the power of his bullets. In game, that part of the weapon applies spell effects (slows, and the snare on his W). But then you have the unrelated spell effects of his traps and the flower effects that have nothing to do with hextech (though his E can be physycal). In game mechanics he has magic in every part of his kit.
In lore, it's stated he's talented at smithing, which implies that he crafts both his traps, and would allow him room to craft his own bullets individually for each target. It's stated his 'gun' is magic (it's referring to the whole weapon, so hextech part is included, but it doesn't specifically EXCLUDE whisper from being magic) It never specifies that he only kills people with the whole thing. So we're at a catch 22.
I'd like to say I don't think magic would make Jhin special. Magic's not a rarity in Runeterra, and is ridiculously common in Ionia. He clearly has some (is stated to) chi abilities (which in RL we'd define as 'magic'). But I feel a narrative and gameplay lean towards him possessing some small amounts of magic rather than none.