He actually mentions significant solar gain on a white structure with partial shade and minimal windows. This is a sign of an insulation problem.
3/4” blue-board foam on it's own does not provide significant insulation you can find better windows. A well insulated house is going to have significant air dead space etc, which makes a huge difference.
Re reading he used two layers of blue board, but I would surprised if he hit R-8 equivalent overall. That fluffy pink foam blocks you see people use are often R-19 and that's in addition to the rest of the wall in a normal house.
Though because it's such a tiny space it's still probably cheap to heat and cool.
Yeah, 1.5" of blue board is probably not sufficient. I imagine carving 4" blocks of foam to fit tightly together would be more rigid and weatherproof, but cutting all those angles just right is difficult.
Sill at 2100$ worth of materials it does not need to last very long and frankly he can toss a tarp over it if there is rain in the forecast.