In a regular DOM there's just a tree of elements, this makes many operations tedious, e.g. finding elements with a given set of classes and so on. So with an inverted-index shadow DOM you get another DOM with element shadows and an index of element properties back to the shadow elements (making it an inverted index). Then simple boolean retrieval can be used instead of DOM traversal. Much more efficient. The actual reason why you want to use shadowing instead of direct-mapped nodes/elements is shadowing enabling E2C (element change coalescing) meaning instead of shadow element changes directly transferring over to a change of the actual DOM element you can batch changes on shadow elements together and change a bunch of DOM elements in one go, which avoids unpartitioned (and therefore wasteful) re-renders by the browser engine.
(Ok, before anyone goes running off telling their colleagues about this great new tech: I literally made all of this up on the fly except the batching stuff. That's actually one of two reasons why this whole shadow-DOM-stuff exists. The other is encapsulation. I think this whole thread is a most beautiful demonstration of Poe's law in its original form.)
I think "shadow-DOM-stuff" refers to the concept of virtual DOMs. The shadow DOM isn't really a virtual DOM though, sure. It's just encapsulated parts of the regular old DOM.