They used a crossover design, so each subject served as their own control. Not a bad choice for trials like this as you gain a lot of statistical power with fewer participants than a parallel-arm, non-crossover design.
I don't think they used crossover design. There is no evidence in the abstract that they used crossover design.
If they used crossover design they should have all participants go through a second trial period where they consume the same diet but with light breakfast and more caloric lunch and dinner. Then they could actually have more insight on the main thesis of their study, i.e. whether bug breakfast alters appetite.
They did a crossover study on the two diets. Ie the high protein diet and the high fiber diet. They did absolutely no crossover or no control on the headline thesis of their paper. The headline being that big breakfast alters appetite or is somehow good for weight-loss.
This study shows or proves absolutely nothing about advantages or disadvantages of big breakfast or that a big breakfast makes any difference whatsoever.
It only shows that if you are going to have a big breakfast as part of calorie limited diet if you choose a diet with high protein you will lose weight slightly faster but will have slightly worse gut health than if you chose a diet with high fructose.
I feel like the regular weight loss group was? Since it isn't necessarily rocket science for having mostly men stay in an easily determinable caloric deficit to lose weight. (Women have usually would be harder due to more conditions and hormone interactions that make finding a TDEE not as simple.)