The poison element across all RPGs is accepted to be a damage over time thing. In League of Legends, this is basically the only thing it could mean, even involving champions that do damage over time that isn't poison (Malzahar, Twitch, Cassiopeia, Singed, Elise, Brand, Swain, and even Darius and formerly Draven). Even thinking of it as "poison" is disingenuous; the element of poison is basically an aesthetic license within the rules of this game, where the only elemental damages at play are physical, magical, and true.
Another way of looking at it is the tabletop route. Poison in Tabletop RPGs cause stat damage more often than not. This type of poison damage is also not new to League. Plenty of champions and items cause stat damage; too many to list them all, in fact. This includes champions and items like Nasus, Trundle, Taric, Miss Fortune, Sona, Vi, Wit's End, Black Cleaver, Ignite, and so on. Bear in mind that this type of poison damage is not synonymous with Crowd Control. This is directly stripping the enemy of their stats so suddenly, they aren't healing as fast as they should, or their attacks aren't hitting as hard, or additional damage received suddenly hurts a lot more. The thing is, any champion that uses a poison aesthetic at the moment doesn't cause stat damage.
These are pretty much the only two things it could be, and if it still isn't, then maybe Repertoir should explain his thought process.