Despite tinkering with Map Range node and mix nodes I just can't produce the same effect. It simply doesn't substract enough and grunge is visible everywhere: 
Hi rrealmtraveler2014 you have forgotten to Clamp the Math > Add Node.
Also be sure that you are using Cycles.
@adrian2301 thank you ! I thought of that when I was outside...AO now works in Eevee, but is not enabled by default ;)
I was tripped up by this too.
The Math>Add node was not clamped at 5:19 in the video. At 5:37 (after a video transition) it is, but it is not mentioned in the narration.
Guys, I'm sorry, but I still don't understand why it's important to Clamp the value of the Math Node - Add (the one where the Musgrave Text is plugged in). I mean I can see what it's doing visually, but what's the explanation? (if I'm not asking fo too much)
Hi Roxana ox ,
No need to be sorry! I'll try to explain; first take a look at the output of the Musgrave with 1.18 added to it:
The AO Node, after it's been piped through the clamped Map Range Node gives values between 0 (much occlusion) and 1 (no occlusion) and these values are being subtracted from above result. When you subtrat 0 nothing changes and when you subtract 1, it shifts down like this:
And clamping the Subtract Node gives:
If we clamp the Add Node we get (before subtracting the AO):
If we now subtract 0 nothing happens and when we subtract 1 (no AO), we get:
and then clamping the Subtract Node:
Here's the file, so you can play with the different values and see what the result is:
https://drive.google.com/file/d/1Zcgbzk0WqFW7B8nPLYWpedWqphxEvFz8/view?usp=sharing
I hope this helps.