Riot, what classifies as a "damaging ability".

I saw that buffed Deathfiretouch ad ratio so I thought, oh man, I bet twitch would be super strong with that! So I tried him out and took it, I figured his passive would apply it, but it doesn't. Then I thought that was fair because that would be kind've op since it was an auto attack, but then I thought- Brand has it, that's a little unfair. Then I ignored all of that and I thought for sure expunge would apply it since it deals damage and is not an auto, but it doesn't apply it either.

So what counts as a damaging ability? Because I'm really confused now.