This treatment kills only temperature sensors, so I'm guessing it would only help with a "burning sensation".

Killing nerve tissue can backfire when neurons higher up start compensating for the lack of signal from neurons below (1). The result can be more painful and harder to treat.

The randomized controlled experiment with dogs was for bone cancer and the treatment appears to increase days until euthanasia about 60% (2). That's a real benefit, but not related to runner's knee, which is often related to the ITB band. For possible treatments, see (3)

1. https://en.wikipedia.org/wiki/Phantom_limb

2. https://en.wikipedia.org/wiki/Phantom_limb

3. https://www.runnersworld.com/advanced/a20844564/treating-itb...