The technique described in the article you linked is actually the use of pig embryos as petri dishes to direct the formation of human organs from cells. No human DNA was inserted into pig cells. The human cells injected into the pig embryos receive the growth signals from the surrounding pig cells, and that is what directs them to form organs.
My main concern is about the source of the human cells. Were they harvested from murdered babies? Or do they come from another source of stem cells, for example placenta tissue? Also, I would have concerns about retroviruses. Our genomes have a high content of retroviruses, which are mostly inert. So do the genomes of most multicellular organisms. While pig and human genomes probably share a large number of retroviruses, they are not all the same. What if an inert pig retrovirus enters human cells and becomes “ert”? What if the pig retrovirus then infects the human recipient of the organs grown in pigs? The potential of pig viruses infecting humans has been a long-standing concern of researchers who have been looking into the potential of using pig organs for transplant.
Of course pigs die for all of this research, but I don’t think there is much concern for them.
This pig embryo was injected with human cells early in its development and grew to be four weeks old. The experiment made headlines when it was announced in early 2017; now, researchers have improved the procedure and tested it on sheep...
...The breakthrough moves researchers a small step closer to growing human organs for medical transplant.”
“To make chimeras, researchers isolate one animal’s stem cells, which can develop into any cell type in the body. They then inject some stem cells from one species into the embryo of another—a tricky procedure to get right...
...Stem-cell experts lauded the human-pig study, but they noted that the pig embryos’ counts of human cells—about one in a hundred thousand—were too low for successful organ transplants.
On Saturday at the 2018 American Association for the Advancement of Science annual meeting in Austin, Texas, researcher Pablo Ross of the University of California, Davis, announced that he and his colleagues have fine-tuned the procedure—boosting human cell counts in sheep embryos to one in ten thousand...
...And to prevent immune rejection, extra steps would be needed to ensure that leftover bits of animal viruses are struck from the pig or sheep’s DNA. But the work shows progress toward more viable organs...
...The U.S. National Institutes of Health currently forbid public funding of human-animal hybrids, though it signaled in 2016 that it might lift the moratorium. (So far, private donors have funded early research.)...
...“The contribution of human cells so far is very small. It’s nothing like a pig with a human face or human brain,” Stanford University researcher Hiro Nakauchi, Ross’s collaborator, said at the meeting. Nakauchi added that researchers are trying to target where human cells proliferate, to ensure that they don’t set up shop in animals’ brains or sex organs...