Thank you for all your replies.
We can see pretty much that this is theoretically and physically impossible, because a battery and a resistor can't occupy the same space at the same time.
So, not only this circuit more than violates--it rapes--Kirchhoff big time, as we have seen, but also cannot have an equivalent version with lumped components.
Now I owe you an answer to your question, what part of Feynman's lectures, namely Chapter 22 is being misunderstood? The short answer is all of it. It is so because people are disregarding basic assumptions that Feynman adamantly stresses in his text.
An answer a little less short is given by Prof. Belcher in his "MIT-quality report" where he elegantly showed where exactly Mehdi, and for that matter all those who still believe that KVL can have the slightest chance to hold under a varying magnetic field, goofed it up. However, after the report, Mehdi continued to espouse his previous ideas, which means that he didn't in fact learn anything. Perhaps, noticing this, even before Mehdi made his second video, Prof. Belcher said in his report:
I am grateful to Mr. Sadaghdar for a number of discussions about Faraday’s Law and KVL, which have improved my understanding of both.
I.e.,
my understanding improved.
Belcher concludes:
Many introductory texts on electromagnetism are not precise about what exactly they mean by the voltage drop across the inductor, and many students come to incorrect conclusions about what this actually means. The most common misconception is that the - LdI/dt voltage read by the voltmeter just above represents a −∫abE⋅dl through the inductor. But if the inductor wires are perfectly conducting, this integral is zero because there is no electric field in the wires.
So, replacing perfectly conducting wires with batteries, or generators, is a noob mistake. It's a trap for young players. This means that the circuit below is not modelling Lewin's circuit.
In fact, Lewin's circuit is not lumpable, because we do not have anywhere inside the loop where we don't have varying magnetic fields, where we could replace the EMF with a battery and get away with it. The voltages that you can measure at the terminals of the resistors of the internal loop are the result of electric fields that are being generated along the very same path where the resistors are.
The failure to understand this basic principle of electromagnetism leads to all kinds of wrong conclusions.