It would be quite difficult to play a video game hosted on the moon, for instance, because the moon is not part of our "now".
If the human brain ran at a slower speed, then our "now" would have a larger effective radius.
When you talk about equal-time coordinates in GR, the notion of now is non-unique, and this is interesting, but popular articles fail to convey this.
When you talk about the human notion of now, the notion of now is local, it's not that this notion of now in astronomical phenomena is different, it's that it can't be defined at all. Popular articles not only fail to convey this, but give the impression that it can be defined. It can't, and that is what is interesting.
There are multiple levels of category error happening simultaneously. The confusion between equal-time surfaces, and neighbourhoods (4-volumes) around points, along with the conflation of a point with its neighbourhood. And from these popular articles fail to convey the interesting properties of either -- the observer's choice in defining surfaces, and that 4-neighbourhoods can't be extended arbitrarily far while preserving their topological properties.
Writing an accurate "popular" article about GR might be impossible, because the topic is so far beyond human experience that only a fraction of the population could ever hope to hold it in their heads.
You can teach people that the concept of "now" is observer-dependent, but as long as we're stuck on Earth, that information is pretty useless. Software engineers working on stuff like global databases and video game synchronization might benefit somewhat from that way of thinking, but they're about as uncommon as physicists.
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.