You can't, of course, see the additional colors that would be enabled by looking at his picture of the gamut, because your current monitor can't produce them :-)

The real question is if the second green is physically realizable with cost-effective chemistry. Given that all real-world sources will start with 3-color RGB, it's questionable whether the improvement would be worth the cost. The Sony F828 camera with its RGBE sensor had the same problem in reverse, there was no advantage to having a 4th primary when everything had to be down-converted to the lowest common denominator.