While the work the authors do is important, in no sense does the tool they produced actually run a simulation.
A simulation implies a physical model and usually partial differential equations that are often solved on supercomputers, but here the neural network is rather interpolating some fixed simulation output in a purely data-driven way.
The simulations have not gotten faster due to neural networks, cosmologists have just gotten better at using them. Which is great!
Edit: see the sub-comment in the thread by crazygringo for the lead author’s take