Paired organ donation is what it's called.

The only living donor without benefit is an alturistic kidney donor. They, nor their family receive anything for it, so they don't do a kidney exchange, they just give a kidney.

This article is a bit misleading or unclear, im not sure if his daughter received a kidney from a deceased donor or a living one or if it was a "paired match" type of donation as you mentioned.

It sounds like his daughter got a kidney, and he, after, decided to be an alturistic donor. But I'm not sure.

https://www.mayoclinic.org/tests-procedures/nondirected-living-donor/pyc-20384850

Edit: looks like it was a living donor scheme so exactly as you said with matching other families. He was doing it in exchange for his daughter. Not to be pessimistic but he did it for a reason. Someone gave his daughter a life changing present and he gave them a life changing present.

Very very few living donors are allturistic ones.

I don't know why but I read up on the most random things.