The definition is truly not a thing that matters. It's the "verticalicity" and "horizontalicity" of the business. Alphabet is very horizontal because they have erm.. Robots.. Internet search.. erm.. Internet services.. mobiles, cars, ... and much more.

So, what should they even write as self-description?

While vertical parts like Google and everything that has to do with it can be described easily, with horizontal parts it's more difficult.

May be that's a reason why each of the big companies have a generic self-description? It's not feasible to describe each of the vertical parts when one is broad in the horizontal, too. And big companies are mostly broad in the horizontal, too..