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.)
Yes, this simulation exaggerates a lot. Either that, or contains a tiny crop of a larger image.