How do I tell if my amplifier is voltage-to-voltage, voltage-to-current, etc
Is probably not helpful to regard this as a voltage amplifer because your input is "soft" i.e. it is a duty cycle but, if the duty cycle control is (say) 0 and 5V in amplitude (standard CMOS levels) then, for a 50% duty cycle you are putting in 2.5 volts and getting out 14 volts i.e. I've just averaged input and output. If your duty cycle were 75% you have an average input voltage of 3.75V and an output of 21V i.e. a "gain" of 5.6 i.e. no different to the 50% scenario.

However, you will have substantial current amplification because your motor is taking 200mA at 50% duty and I bet the current taken by your PWM input is in the realms of micro amps.

But, after saying all of that I don't think it's helpful to regard this amplifier as having anything as straightforward as voltage or current gain.