Why use PWM signals?
It appears they are trying to avoid noise. I found an open (legal) copy of their paper on the NCBI website


  However, analog samples are susceptible to noise, and the transitions from one channel to another in short sampling periods can result in significant crosstalk among adjacent channels on the receiver side


This is for implantable devices with the signals going directly to RF. Adding an ADC as suggested in the comments would be counter productive since then a microcontroller would have to read said ADC and then modulate on the signal.

doing a direct AM or FM would likely be difficult since the values are so small and they are multiplexing 15 channels. by going to a PWM they get a digital representation that they can send using Phase Shift Keying (PSK) which is 'digital-like' in that the value are very distinct 1/0 (0 deg/ 180 deg) over the transmission medium. Since they need low power the more distinct the signal out the better.

In short they get the value of a digital representation without the added cost of digital components