While an interesting analysis, it only really deals with economic efficiency. What really matters is how good the various types of empires are at increasing the strength of their economy, their economic growth. This is the area where gestalts, and especially machines, suffer.
Because normal empires have ruler pops they're going to run into amenity problems much later, and even when they do they have a lot of tools to address the issue. They can throw consumer goods at the problem, with the decision, they can build holo-theatres, gene clinics, or housing buildings. Gestalts run out of amenities quicker and have to go to maintenance drones to get more, which are inefficient.
Machines, however, face even more problems. A major offender is that their pop growth is expensive. Organic empires get 3 growth per planet for free, machines have to pay 9 minerals per planet to get 3 growth. Ouch. That's a lot less minerals for constructing buildings or producing alloys and research.
At least hives get extra pop growth to make up for this. I can't say whether hives' bonuses are enough to make them better than normal empires or not, since I haven't experimented much with them, but it's definitely within the realm of possibility. Machines get perfect habitability, as well as pseudo-immortal leaders, which doesn't come into play until the mid-game. Their habitability bonus is nice, but sadly not enough to make up for their shortcomings.