The author of the article is welcome to compute the mass density of the atom's periphery to the nucleus, and return to speculating whether it's fair to argue that the atom is mostly empty space or not.
For myself, I'm happy to refer to ethereal probabalistic cobwebs as "mostly" empty space.
As a thought experiment: If you have a peach, would you declare the fleshy part non-existent once the pit achieves a certain mass density?
The actual scenario is this: "If you have a peach, would you declare the fleshy part non-existent if it had a certain probability of reallocating itself to a single spot once the pit achieves a certain mass density and if you touch it, there is only a small probability that you can even feel that the flesh is there?"
The entire electron cloud produces an electro-repulsive force that is very real. That is what you feel, there's no small probability about it. This idea that there's some small probability that you hand will go straight through the table is ridiculous.
When you touch a peach, some of your electrons/atoms actually do become part of the peach and vice-versa. If we somehow turned up the tunneling probability, your hand would not go through things, it would simply dissolve into things more readily.