Vayne is the better single target DPS version of Kog'Maw, Twitch is the multi target DPS of Kog'Maw
And Kog does both at the same time, with more up time for his range than twitch, and more range than Vayne. If you can build your team around protecting him, and you do your job well, he can shred the competition(aka - the enemy team).
I mean, why play
when she has worse heals than
, worse damage than
or
, less peel than
, and less cc than
? Its because she does all of those things at a passable level, and is great if you can't decide which would be most useful(say if the adc hasn't hovered a champ yet, and its your turn to pick).
Kog's obviously a different story, but if have a team without high damage but your team has a ton of cc and peel(

for instance) Kog would be a good pick because your team could enable you to sit back and decimate the enemy team in a way that
would have to endanger herself to do(and Kog is easier to play correctly) and going twitch would mean only being able to do that multi-target dps for 5 seconds every 90 seconds, while Kog can do it for 8 seconds every 17(with cdr it is enough for multiple times a fight,). Kog also has the advantage of a long range execute, which is able to be cast multiple times, and prioritizing on-hit/attack speed which gives him mixed damage, witch is harder to itemize against than twitch's pure ad+small amount of true damage(which is answered by any ar +health item).
And before you say "oh
has mixed damage_ too_", may I remind you that Corki is short-medium ranged, not considered a hyper carry, and does not do % max health damage without itemizing for it.
So that's why you would take Kog over Twitch/Vayne. He does so much more than either of them, providing that your team keeps him alive(i mean, why else would pro's use "protect the Kog" comps if he isn't useful?).