Why is it considered core Vayne?
For a long time Vayne's core rush item was
because the life-steal is a life-saver in her lacking lanning phase.
Kingblade gives life steal and AS, which helps a lot early game.
Also: Kingblade's mixture of AD, AS, life steal, and the burst-damage nuke offer a nice package for a good power-spike with 1 item: which goes a long way to solving a lot of Vayne's early-game woes. With Kingblade completed she becomes a solid champion. Vayne also scales so incredibly well with items late she doesn't have any bothers to give about trading a small bit of late-game hyperscaling for a good chunk of early-game power. LoL isn't 100% about the late game, quite possible to loose a game in the mid-game and early-game stages.
%HP damage not scaling with crit or AD doesn't really matter when it automatically scales itself based on the HP (or really level) of your opponents anyways. It's not something like Wit's End flat damage were it actually does kind of fall off. Vayne isn't giving up much late-game power for that.
Lastly, Kingblade offers a lot of great tools to reliably and decisively deal with tanks and tanky DPS champions. Their main weakness is being kited to death, which the %MS slow really helps a lot with. Many tanky champions also tend to be more sustained DPSy than pure-burst, allowing life-steal a lot of potency in dealing with such champion to make Vayne deceptively hard to kill.
%Hp damage is icing on the cake, but Vayne would still grab Kingblade if it didn't have that.
TLDR: Kingblade offers Vayne a huge power-spike 1 major item in.
Vayne generally sucks 1 major item in, and her main weakness is loosing the game before she's amassed 3 major items.