Dish soap does NOT do that. (It's also why you shouldn't wash dishes by hand with dishwasher detergent, because the chemicals are too harsh.)
I don't doubt that this "hack" does some cleaning, but for things like crusted-on tomato sauce, hardened cheese, dried egg yolks, etc. -- it's just not going to work as well. Dish soap simply doesn't break these things down. It's not meant to.
(Washing by hand with dish soap works because you're applying intense pressure and abrasion, neither of which a dishwasher can do -- which is why it does it chemically instead.)
I just don't find it credible that "the results are identical". Either the author isn't paying enough attention, or else they're doing extensive "pre-washing" of their dishes before loading them, or they're washing so incredibly quickly after eating that food never has the time to dry/harden in the first place.