I've always hypothesized that it's the fact that you can't eat most junk food. No chips, soda, candy, rice, bread, etc. Most fat people are eating too much of those things. I bet if they did a Keto + reasonable amounts of carbs in otherwise healthy dishes, they'd still be losing the weight.
The benefit of keto is more satiety than anything. All diets use calories deficits but on keto I'm not nearly has hungry as I am on sugars or starches. Chicken and rice vs chicken and broccoli and I'll take the latter.
That's generally what a keto diet turns into once you've lost your target weight. I eat carbs now but still try to keep them as low as possible and it's great to maintain my current weight.
If the (surprisingly large amount of) anecdotal evidence on /r/keto and similar messageboards is anything to go on, keto is very effective for losing a large amount of weight, possibly the best dietary strategy. But I don't think anyone really knows why.