alt Hacker NewsNoise 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.