Summary is she received a liver transplant and because of some details discussed in the video, she has her donors blood. Since her donor was male, does that mean his dna, and only his dna, is found in a sample of her blood?
First simplify this - end result was that is in the same place as a successful bone marrow transplant individual.
The blood cells, including immune system cells, are all from the donor, but the rest of the body is still host and there will be cell free DNA fragments floating about. Some of those fragments will be of sex chromosomes and mitochondrial origin. So not “completely” … but all DNA from whole cells in her blood, just as in a bone marrow transplant. Testing using a swab from the inside of her cheek (buccal swab), spit, or most not liver tissue biopsy, mostly her original female DNA.
I’ve heard of cases when a bone marrow recipient has two sets of DNA, one being from the donor. The technical term for this is chimera. This New York Times article (gift link) describes one case where the recipient’s semen only has the donor’s DNA.