Does the importance of understanding how an engine work disappear when a different type of motor is substituted?
The importance of understanding how your aircraft works, not just the "motor," never goes away. Systems knowledge is far more than theoretical rubbish.
In the case of your piston power plant, understanding the operational theory is basic to understanding leaning, carburetor ice, manifold pressure and it's applicability to setting power, fuel flow, the impact of a constant speed propeller, etc. These, in turn, have direct bearing on the handling of abnormal and emergency situations.
In a fuel injected Continental IO-520 in a Cessna 206, for example, one may see a high fuel flow, and feel that one should retard the mixture in flight. At first blush, this appears the right choice, to bring fuel flow back to an acceptable value. The problem is that if one understands the fuel flow indication system in that airplane, one will know that fuel flow is determined by the pressure drop across the fuel injector nozzles. A plugged injector means a lower fuel flow, which indicates as a higher fuel flow. At high power settings, where the greatest disparity will occur, retarding the mixture is exactly the wrong thing to do; one may well damage the engine, or cause it to fail. In this case, knowing your system may be critical to your health.
As you can see, there's a lot you can do in the cockpit about engine problems, whether it's the way you address them, or the checklist you choose.
Systems knowledge, whether it's your engine or your electrical system, is always important. This is true whether you're flying a Cessna 152 or a Boeing 747.