Damage done to champions can be a very misleading stat and which is one of many good reasons why champions are only compared to the same champions for the Mastery Grade. Kills aren't necessarily linked to damage dealt to champions.
You did have more kills and you both had about the same amount of deaths, with you have having one death more while you both are playing champions with late game scaling.
However, for Vayne, the majority of her deaths are in the 1st half of the game, where as the majority of your deaths as Kog'maw were in the last half, where death timers are longer. This means that for those deaths, you were spending more time off the field for each one and that these were occuring during the time of the game when the DPS for the champions is going to be significantly higher than it was previously, especially for Kog and Vayne, due to them having more items, far higher than the times where the majority of Vayne's occured.
So no, this game's Damage Dealt to Champions stat is not due to, is not evidence of Kog'Maw under-performing, whether he is or not.