Some simulations also use Smoothed Particle Hydrodinamics (see here[0] for a simplified example), like the Earth-Theia impact Moon simulations[1]. However I'm not in the field and can't really tell how much this kind of code has been used lately, but you did remind me of it when you talk about this simulations being monte carlo sampling of stellar mass distribution, because SPH has some concepts like that "inside" the particles.
Also, for everyone to enjoy simulations results, check the simulations by Canup from the giant impact hypothesis[2]. Another thing to consider, the supercomputer used for this specific simulation had about the same computer power as a high end GPU from today.
SPH has been fairly common in galaxy simulations over the past 20 years or so. But there's some glaring issues with "classic" SPH formulations, to do with fluid instabilities. As a result, lots of people are transitioning to moving mesh codes. I put a few links in my other comment (https://news.ycombinator.com/item?id=12461336). I'm pretty sure the simulation in the press release is also using a moving mesh for the hydrodynamics.
GIZMO is the name of the code suite, not the numerical technique. I believe GIZMO contains multiple hydro solvers, including various formulations of SPH, moving mesh, and meshless techniques. But you're right. that the simulation in question wasn't a moving mesh, it was a meshless technique.
Also, for everyone to enjoy simulations results, check the simulations by Canup from the giant impact hypothesis[2]. Another thing to consider, the supercomputer used for this specific simulation had about the same computer power as a high end GPU from today.
[0] https://benedikt-bitterli.me/bbw.html
[1] http://lasp.colorado.edu/~espoclass/ASTR_5835_2013_Files/201...
[2] http://www.boulder.swri.edu/~robin/moonimpact/