First, it needs to be clear that what happened was the growth of kidneys in pig embryos. This has not gotten to the point of full sized organs in a pig that's viable.
Second, this is a single step along the much more difficult path to growing human or humanized organs in pigs. While it is pretty damn huge news within that research, it's nothing we're likely to see turn into a patient available technology any time in the next twenty years.
What they did was find a way to get a pig embryo to grow kidneys that are humanized. This means that they're mostly human cells, but not entirely. Vascular cells in particular remain porcine.
They did this by erasing the genes for kidney formation from the original cells, then inserting human cells. Without the code to grow its own kidneys, the embryo doesn't block the attempts of the human cells to do so. They then fill that role.
The embryos are then harvested and examined, and we get the data filtered through the science writers. Alas, even the Guardian uses flashy headlines, so it looks like something other than what it is.
The real headline should be something like "key step in research towards growing human transplantable organs in animals achieved." And it is a key step. But it's maybe step 10/100+