One of its marketing tools was Play-Create-Share.
You have nailed the subject here, marketing.
As much as you aspire to argue that LBP is not a platformer at its core you are still failing to provide any evidence that it's not. In my account, I have only played LBP 1 and I base my opinions around such.
3 LBP games. All 3 have developer curated platforming single-player and MP(CO-OP) that revolves around its mascot, Sackboy, on a quest to save "creativity from some evil dude". The developers didn't design a FPS in a World War setting, nor a TPS as in Uncharted, nor a stealth game, but a mascot platformer. Now that can't be refuted by conjecture, marketing selling points or any other type of spin.
Somewhere down the line while pitching LBP Media Molecule realized that it would be cool if they could tweak their engine and give players the ability to create their own levels with various tools. Not only is this a major differentiator (marketing wise) from other platformer offerings but it also extends the life of the game and allows for neat creations from the community - A WIN WIN. LBP level editor is the simple solution to the old platformer's debacle (if you don't like how we design our levels, or got tired after your playthrough - create your own, and while at it, share them too). It obviously evolved to much more - some of it unintentional.
In LBP 2, following the overwhelming popularity of its slogan, and the use of their tools by the community, Media Molecule simply rode the ship and doubled down on expanding this popular part of the game which still serves as a major differentiator for platformers out there.
Still, at its core, LBP is a 2.5D platformer that reviews as a platformer till this very day. It reviews as a platformer for a reason - it's one.
I alluded to a simple idea: any competent engine out there can do more than just the genre developers that use it usually heavily focus on. For example: You can make platformers, FPS, TPS, Stealth games, you name it, you can make any of that with the Unreal Engine, the Frostbite engine, with CryEngine etc etc. It's all about the feasibility of giving players the tools to do so. Obviously I am not saying all complex engines can be shrunk down to peasant accessibility. Just the logic.
There is a difference in the core competencies of both games. You can not equate the two, despite there being somewhat of an overlap - by accident and design.