The point is that our next relatives on the tree of life are very similar to us in many ways but we would nevertheless consider them pretty stupid. Pretty much all impressive human achievements will be forever inaccessible to them. DNA is just a very striking way of illustrating that similarity with the one big difference.
It is similarly imaginable that evolution could, without breaking a sweat, spit out intelligence that would consider us stupid the same way we consider chimpanzees stupid. They can do some cute tricks but that’s about it.
He basically wants to open our eyes to the idea of a vast scale of intelligence, not between village idiot and Einstein but spanning much wider. Meeting someone that is just as intelligent as we are seems unlikely.
I understood what he meant, I just didn't understand why DNA was helpful in illustrating it. I'm a lot smarter than a nematode, or a pebble, or a cell in Conway's Game of Life. The number of base pairs I share with any of those things (where applicable) is irrelevant.
