Why? Why does this kind of culture crop up again and again in human history?
I think because ruthless internal competition offsets some of the natural lethargy of a bureaucracy. It can serve the interests of whoever is on top, at least in the short term. If you have no talent for inspiring people you can at least set them against each other. But you'd be a fool to join such an organization at the bottom, knowing what it is, if you had any alternatives.
I like how you mind works, BTW. It is an interesting question to ask.
In the short term, as you point out, it does serve the personal power of those on the top. The ruthless backstabbing leaves those with real power apparent freedom to make completely arbitrary decisions at any time, by providing ammunition against everyone so there are scapegoats aplenty.
In the long term, the culture of infighting becomes the de facto entrenched bureaucracy, where you re-create approximately all the usual negatives of bureaucracies. In TFA, we apparently have a manager that everyone is too scared to even give a good hard slap on the wrist, because he has played the politics well and has successfully carved out his fiefdom.
Furthermore you fail to achieve the positive advantages of bureaucracies. In physics, inertia is a component of momentum whereby an organization has some degree of certainty that they can continue heading in a direction -- continuing to go sort of in the right direction is usually better than standing still or spinning in circles. That allows a company to make and keep promises, both to themselves and to their customers.
The reported cowed HR, the fiefdoms, the nasty politics, the lying on reviews, the constant fear of re-orgs, the failed projects -- these do not sound like a cooked up list of accusations. They are very much self-consistent and self-reinforcing cultural behaviors that you would expect to find together in the same organization.