That’s just a mistake, should be:

s’agrippe à ma première canine,

Curiously, another print of this text has a different mistake on the very same word:

Looks like someone over corrected it.

What or who is the subject of this imaginary action?

-> La serveuse

la serveuse s’agrippent à ma première canine.

la serveuse, short description of the action (s’aggriper), s’aggripe à ma première canine …

subject + short description between commas + conjugated verb + end of the “sentence”

for example the same meaning :

La serveuse s’aggripe un instant à ma première canine

But the rythme of reading wouldn’t have been the same

Obviously the the next It doesn’t work (just shitty commas that could be dots but dots would divide too much the actions) :

… ma première canine, images folles, je me pince.

Here ->

ma première canine : end of the sentence (not a subject)

images folles : just a feeling (“that’s crazy”)

je me pince : action (“I pinch myself”) (subject + conjugated verb)

I hope I have been clear enough in the explanation