If the universe were an aggregate being, made up of tiny non-sentient components with an emergent consciousness, then why are we -- tiny ourselves -- also sentient?

I understood it to mean not that we, also are conscious, but that we are the conciousness. In fact they specifically said: "We humans, as the consciousness of the universe...".

Plus, if I am aware of my finger I can wiggle it. But how can we be 'the universe becoming aware of itself' when we are not really connected to anything else, and are totally unable to affect the rest of the universe?

I don't see that there's a contradiction here unless you take them to mean that we are the entire universe. Don't think they said that either. We are a subset of the universe. We can do what we can do and be aware of what we can be aware of. And if the universe can be said to contain any self-awareness, then we are that part.

You aren't saying we are outside of the universe, are you? That would be an extension of the belief that humans are not animals, which some religious folks do believe.

Had to read it quickly, so I may have spaced the part you keyed in to.