Why does this circuit work?
... I can say that Ic = 100*(3.3/1000) = 0.33 Amps.


Incorrect. You can say that Ic has a maximum of 0.33A (or whatever it would actually be with the correct values and formulae). If the supply isn't actually capable of supplying that much for any reason then the transistor is operating in saturation mode, where it acts as a switch. Which is exactly what we want it doing for operating a motor.