me havent watched whole video, just the second half. But i dont think it was any special operation, just curious or cruel scientists. They made dog's brain starving for 10 minutes, what in most cases damages brain, similar as drowning. Then they substitued his hearth and lungs with fancy machine for some time, finally connected his brain back to old hardware... But most of cells in his body would die after much longer time than 10 minutes, just most sensitive are neural cells ofc, which needed some substitution of oxygen source.
If you would get lung failure in hospital with perspective of fast transplantation, they would do similar operation, just not disconecting your brain from rest of the body, like in case of poor dog.