How does Alistar deal so much damage in this specific match?

I've played this match where I went full AP Malphite vs full AP Alistar in mid lane. We do the occasional trades but I lose more HP than Alistar does. Yeah I know, I'm retarded for playing full AP Malphite.

Alistar isn't suppose to be a huge damage dealer right? His only 2 damaging abilities is Q and W but I just can't wrap my head how he is chunking me for half my HP everytime he does the W-Q combo. I'm also talking about early to mid game only. He has Thunderlords, Hextech Revolver, and Ignite, but that's about it for all the damage sources he has in his disposal. Yet, as he roams, he's chunking my teammates health away and killing them as well, which makes me even more confused. His KDR is huge.

The thing that confuses me the most is, Malphite has almost both the same base damage and crappy AP ratios as Alistar does, but he can be able to chunk my HP more than I can be able to chunk his.

If anyone can help me theorycraft this, I will truly appreciate it. I am a bit tilted by this (as well as having a losing streak atm), so I really apologize if I sound desperate.

Here is the match where I screw up on. http://matchhistory.na.leagueoflegends.com/en/#match-details/NA1/2204660514/227209361?tab=overview