>>14078458small-signal model != small signal amplifier
Regarding small signal class-A amplifiers configurations I would say it's the fixed bias circuit due to stability factors. If OP pic related is the small signal model you probably can't determine which configuration is being used.
Nevertheless, if OP pic related IS the actual circuit (not just the model) then indeed, it's the shittiest way to amplify a signal. Unless if it's being used as a digital signal inverter (which I doubt bc the analog signal draws at input and output).
You made me look through my old books, I hope you're happy now.