This GR thingy holds for every observation, even those here on Earth, but there the time-delay is small enough that we can ignore it. But if you think of it as the first stretch on a very long gradient all the way out to the stars where that difference becomes more manifest then what these researchers have just done is shown you is to prove that the gradient exists on every level of scale, likely all the way down to the interaction of two atoms in a gravity field, but for now we have it down to a mm or so.
This is a super impressive result and it makes this concept a lot more accessible than the 'Earth time is special' vs 'interstellar distances are in the past'. They're all in the past from the point of an observer, even if that observer is a few mm away from the event.