It is not quite accurate to say that they have Zodiac's DNA. They have DNA (a partial profile) from a stamp from one of the letters mailed by the person claiming to be the Zodiac. It is likely, but not certain, that the person who sent the letter licked the stamp, and it is highly likely that most of the Zodiac letters were sent by the actual killer. In other words, they have a partial DNA profile that probably came from Zodiac.
They also have some hairs that came from Cheri Jo Bates's bloody hand; those probably contain mitochondrial DNA (as opposed to the nuclear DNA from the stamp).