The beats aren't as strong as when two slight variations on the same note are played. But they are still easy to hear in that link.
How come people use tuning forks and pipes for tuning?
Since most of the energy in a note is at the pitch the note is theoretically at, this is easy to hear when comparing a pure tone to a normal musical instrument with lots of harmonics. Furthermore it is actually somewhat harder to hear it than when you are comparing two musical instruments that both have harmonics, because you get more complications you need to ignore in the harmonics when you're listening for that conflict in the base note.
Well, yes, that's the point of my question. If harmonics were essential to the concept of "in tune", we wouldn't tune by using an instrument that has essentially no harmonics.
Perhaps if you explained your confusion more, it could be answered better.