First of all, interesting question, and thanks for sharing the video!
Secondly, you write:
There seem to be no doubts that she has the same perception of music than any other great musician...
I have to disagree. She may be able to sense vibrations, but it can never match normal hearing. This, because the human ear is better equipped to analyze acoustic sounds than the tactile system. Acoustic frequencies can be heard between 20 Hz and 20 kHz and maximum sensitivity is at 4 kHz. The tactile sense has a lower minimum, but its optimum lies at 250 Hz, and the maximum at approximately 500 Hz. Hence, the human ear exceeds the tactile system by 5 octaves. More importantly, however, is the exquisite sensitivity of the human ear that outperforms the tactile system in orders of magnitude.
In effect, the musician can acoustically feel only tones of low frequency of high loudness. What she can pick up is the tactile sensation from playing the instrument, however.
Note that Beethoven was deaf, and composed master pieces. Importantly, both Beethoven and Glennie were not congenitally deaf, but lost their hearing later in life. Hence, their sense of acoustics was already shaped, and my guess is both relied heavily on their memory of hearing.
To translate the acoustic dynamic range into a vibrotactile one, one would have to compress the acoustic dynamic range onto the vibrotactile dynamic range. Frequency compression is exactly what has been done in vibrotactile devices that substituted hearing for touch. One example of such an approach is the TickleTalker. This device was designed as a vibrotactile hearing aid to increase speech recognition in the profoundly deaf. Although the idea worked, it never became a success (Cowan et al., 1990). In general, sensory substitution approaches suffer important drawbacks (see why-is-sensory-substitution-not-that-successful).
An important factor with the TickleTalker is that the frequency range as well as the frequency resolution of the ear is much better in the ear than in touch. In turn, the quality of vibrotactile hearing is inferior to acoustic hearing.
However, the biggest factor in the case of vibrotactile hearing substitution not being successful is the fact that cochlear implants are very effective in restoring sensorineural hearing loss. Cochlear implants directly stimulate the auditory nerve, thereby bypassing the defective hair cells, the most common cause of deafness. Note, however, that brain stem implants and cortical implants are used as well, that together cover nearly all causes of deafness. Hence, these devices actually restore hearing in deaf patients. The resolution is not too great (7 effective frequency channels, give or take), but speech understanding scores in cochlear implants users is overall remarkably good. Some are even able to talk over the phone.
- Cowan et al., Australian Journal of Audiology (1990)