With the disclaimer that I am comparing to the memory of some entry-level cameras, I would still say that it's way too noisy.
Even on old, entry-level APS-C cameras, ISO1600 is normally very usable. What is rendered here at ISO1600 feels more like the "get the picture at any cost" levels of ISO, which on those limited cameras would be something like ISO6400+.
Heck, the original pictures (there is one for each aperture setting) are taken at ISO640 (Canon EOS 5D MarkII at 67mm)!
(Granted, many are too allergic to noise and end up missing a picture instead of just taking the noisy one which is a shame, but that's another story entirely.)
Noise depends a lot on the actual amount of light hitting the sensor per unit of time, which is not really a part of the simulation here. ISO 1600 has been quite usable in daylight for a very long time; at night it's a somewhat different story.
The amount and appearance of noise also heavily depends on whether you're looking at a RAW image before noise processing or a cooked JPEG. Noise reduction is really good these days but you might be surprised by what files from even a modern camera look like before any processing.
That said, I do think the simulation here exaggerates the effect of noise for clarity. (It also appears to be about six years old.)
The kind of noise also makes a huge difference. Chroma noise looks like ugly splotches of colour, whereas luma noise can add positively to the character of the image. Fortunately humans are less sensitive to chroma resolution so denoising can be done more aggressively in the ab channels of Lab space.
Yes, this simulation exaggerates a lot. Either that, or contains a tiny crop of a larger image.
Yeah, I don't think that it's easy to reproduce noise (if it was, noise reduction would be even better). Also, bokeh/depth of field. That's not so easy to reproduce (although AI may change that).