Is there a way to find out how much traffic, in absolute numbers, a website gets, if I am in no way affiliated with the website in question?
You could find out who is hosting the site and ask them really nicely. 
Seriously, there is no way of doing what you want without rerouting some pretty fundamental parts of the Internet’s infrastructure (physical or logical).
How do ranking sites find out the traffic of the sites they rank?
It’s the web version of a Nielson box. People install software that tracks their usage in exchange for swell prizes. This small sample is then used to extrapolate overall statistics.
You can follow a sample of users around. You can get these users ethically or not (spyware). You can pay people, Comscore and Neilsen both have large panels of users they follow around. Websites can also self-report, and have those results audited. My companies numbers are vetted by I-pro, who looks at our log files once a quarter to make sure we’re counting in the correct way.
All of these share some common issues with counting though - it’s almost always cookie based, and that creates problems. Users might not cache cookies. You might look at a site once from home and once from work. A library terminal is shared by multiple users. There’s actually a lot of fine points to counting, web analytics is based on some shifting sand.
That said, there’s a lot of difference between trying to find this out for a large or a small site. What are you looking at?
I think that Alexa has what you’re looking for.
A number of small sites.
I only found ranking there, not absolute numbers. Where is it?
I think for small sites, you’re probably up the creek. User samples won’t do it, so they would have to be self-reported numbers.