Yeah this is exactly how I think of it. I think "graphs" are just at a different level of the abstraction hierarchy than the data structures they're often grouped together with.
This is even further up the abstraction hierarchy, but to illustrate the point, nobody really wonders why languages don't ship with a built-in database implementation. And it's the same basic reason as with graphs; one size doesn't fit most.
Well, the original article actually describes that relations are great way to model graphs, and suggests that your language (or its standard library) should ship with a good datastructure for relations.
You would get most of a what you need for a simple relation database this way.