Why (or how) is this different than the Pound-Rebka experiment? (done 59 years ago)
Each new proof of GR necessarily puts a hard experimental limit on the kinds of theories that can replace it.
I think we are in agreement here. Some of the current theories have to be or have been discarded because they failed to predict what has been measured.
This paper talks about binary pulsars (circa 2008) and how experimental results have confirmed GR and limited other alternatives to GR:
https://books.google.com/books?id=sT_ICgAAQBAJ&pg=PA225&lpg=PA225&dq=GR+experiment+limits+alternate+theories&source=bl&ots=fFcBpAKvnS&sig=7XeNlFIe-Q-SQCkS7ppedB-ALc4&hl=en&sa=X&ved=2ahUKEwjTg7WisL_cAhWI7IMKHbZqAO0Q6AEwBnoECAUQAQ#v=onepage&q=GR experiment limits alternate theories&f=false
My guess is primarily because it was done at larger scales and more extreme conditions around a black hole whereas Pound Rebka was done in an Earth laboratory.