What is a transformer-coupled class A amplifier?

A transformer-coupled class A amplifier is just what it says it is. You'll recall that a class A amp is one that has an output that varies through all 360 degrees of an input signal. As regards the manner in which the signal is coupled to or from the stage, a transformer is used, complete with the non-linearity that it will introduce because of the characteristics of the (untuned) inductive component.