I will start by saying that I have no idea what their plans are and I am not a game or game engine dev.

how do you have the same skin in multiple games for different character or items models?

I think what we'll see is the model and mesh of the skins will be loadable by the game via the engine. I'm assuming they'll have a standard that contains the hitbox and model/mesh to put on the character. Then the game dev could tweak gobally the scaling (as an example) to make all skins fit nicely into their game. Same for guns and such. But game devs who want to opt in[1] to this will have to use the engine API to make it work.

Are they going to update every game when there is a new skin released

I would assume that the game itself won't need to be recompiled or updated but rather the engine will download the newest skins in some common and reusable place. And then the engine swaps one model for another.

[1] my suspicion is that the tech will be licensed to the game makers. Especially if they plan on allowing copyright characters (like Marvel characters).

And again, please take everything I said with some salty grains or something as I am only speculating.