This appears to be a transfusion of mature blood cells derived from donor CD34+ hematopoietic stem cells, and it sounds like they're able to collect usable numbers of stem cells from a regular unit of whole blood... but how?

People normally don't have a whole lot of stem cells in the peripheral circulation (if they did, they'd have leukemia). For the purpose of stem cell transplantation, the donor is given medications to mobilize stem cells from the bone marrow before collection. I'm sure they're present in very small numbers in the blood, and perhaps they could be cultured in the lab, but even stem cells become exhausted eventually. This is the innovation, probably.