What I take away from the video is that they don’t make actual contact. He’s defining a contact point as the point where they get close enough to repel each other.
It might be different if an atom were a simple solid piece of matter but it isn’t. If a hydrogen atom had a nucleus the size of a basketball, it would have an electron orbiting nearly a half mile away. If you have a neighboring atom, it doesn’t seem possible that their electron orbits can cross or there would be chaos and the atoms would destroy each other. (Electrons smashing into each other or into the nuclei of the neighboring atom)
“It might be different if an atom were a simple solid piece of matter but it isnt.”
We have known the Rutherford model of the atom is not accurate for some time, so why bother talking about atoms as if it were? It seems more accurate to say that “solid matter” is an effect produced by atoms, like an emergent phenomenon, and not an attribute of the atoms themselves.
So, do the atoms touch? They not only touch but they merge. Do the nuclei touch? No, except under very unusual circumstances, but that is a very different quetion.
I think it’s the way you describe in metals. A mess of electrons swinning around everywhere.