This is not noise but grain and there is a huge difference!
Noise is an unwanted digital artifact caused by electronic... noise while grain is used during post-processing on purpose to add some style to a photo.
One can like or not grain (I do like it), but it is an artistic choice from the photographer and should not be seen as noise IMHO.
In this case, the grain is used to give an aged look to the photo along with the sepia toning. This is not the prettiest grain I've seen however

Have a look at any old B&W photography or even at many movies (did you see 300 recently?) and you will see a lot of grain and this is often just beautiful while noise is just awful.