They led the teams that gave the decisive proof that there is black hole at the galactic centre. The teams developed techniques to precisely measure the orbits of the stars which orbit the central black hole. Looking at the speed of the stars, particularly as they pass close to the object, you can measure its mass and put a constraint on its size. The only thing which is small enough and heavy enough is a black hole. Doing this required lots of advances in data analysis and adaptive optics to be able to measure the stars orbits to enough precision.
Their work goes back 30 years.
Too late for Hawking indeed, he could've very well been one of the winners today.
However, the Nobel committee's rules can be considered archaic to a fault: 3 winners at most, all winners must be living at the time of the award.
If you want an egregious example of exclusion, look at the 2013 Nobel prize for the discovery of the Higgs boson. The prize was given to Higgs and Englert [0], but by any measure it should have been awarded to the five living scientists who made the discovery [1].
Was there really any reason to exclude Guralnik, Hagen and Kibble, who were all alive at the time of the award, other than a strict adherence to the "rule of three"?
[0]: https://web.archive.org/web/20131008193310/http://www.nobelp...
[1]: https://en.wikipedia.org/wiki/1964_PRL_symmetry_breaking_pap...
I haven't found an updated GIF, but even when I first saw images like this around 2002, it was clear she was chasing something awesome.
https://www.physicscentral.com/explore/people/images/2008orb...
Fun fact: looks like we're both in MPE (although I left two years ago).