"While it is true that pigs are less compatible with humans than monkeys, they can be genetically manipulated to produce organs less likely to be rejected on transplantation. Pigs quickly grow to full size, produce larger litters and can be more easily reared by biotechnology companies."

They do cover this point.

That's pretty clearly explained in the article.

Pigs have a lot of physiological similarity to us (thus why fetal pig dissections are often done in high school/undergrad biology). Plus there are fewer ethical concerns around using an animal we already use for food.

I imagine there's also a consideration for ease of raising. These pigs had to be kept separate from others and tested frequently for disease because of having some aspects of their immune system weakened to reduce rejection risk. This would probably be easier to do ethically for pigs compared to primates.

Pigs are not too far off when it comes to the overall body. I believe the idea to use a pig's heart is one off availability (and maybe ethics). A ton of pigs are slaughtered each and every day, we already use several parts of a pig's body (which is a good thing, waste as little as possible). If we can successfully use it's heart for transplantation, even better. This means there is a good supply of hearts to be used.

Read the article.