Please don't take this personally this is just one chef critiquing another closely considering it's out there to demonstrate how to make pasta.
Ok, I'm not too sure Joe was the same person that wrote that recipe but both the written recipe and Joe's technique leaves a lot to be desired.
He used whole eggs and put nothing else in the flour, yet the recipe when you look at the directions it says to add the yolk and whole eggs, obviously it's a combination of both, which is quite popular, plus evoo and a 1/2 cup of warm water and some salt. Plus an extra 2 tsp's of water but that never gets mentioned in the directions. As well as a 1/2 cup of warm water, why? makes no sense.
Also when making pasta the general rule of thumb is for every 100g's of flour you add 1 egg so 3 cups of flour they call for 3 eggs. The problem here is depending on how you handle the flour a cup a flour can have different weights and why it's always recommended to weight the flour out. This is where the 2 tsp's of water would normally come into play. Because the weight can fluctuate when using cups it may require a little water to bring the dough together. Unfortunately that whole methodology just got lost but they put in the 2 tsp's as if they thought they should because maybe they read it somewhere but obviously didn't really know why.
Ok, sorry I just can't let this slide. When Joe starting bringing the dough together he proceeded to fold the dough over upon itself and then pushed down on it and repeatedly did this and actually explained why he did it, yeah, no, not in any kitchen let alone anywhere in Italy would you see someone make pasta dough like that. He just handled the dough like it was his first time making pasta.
The dough he produced was far too wet and kept incorporating more flour into his dough and then when he rolled the dough it was literally covered in flour and was too soft and thick. then he just unrolled it and dropped the pasta in the water without letting the pasta rest for a period of time. There's more but I'll stop there. The whole demo was a tragic mess. Of course this is just my opinion and if he was in my kitchen I would have delegated him to the dish pit and kept him away from the food.