When you're engine braking—like when you downshift and let off the gas—the ECU often cuts off fuel to the cylinders. The throttle valve is also closed. In this scenario, your RPMs are maintained by the car's forward motion, which is connected through the drivetrain back to the engine.
So yeah, you're not using any fuel in that case, but you're still turning the engine over. The wheels are essentially driving the engine instead of the other way around. That's how you can have RPMs but no fuel flow during engine braking. The energy to keep the engine turning is coming from the car's inertia.
A common example would be going downhill. You downshift to a lower gear, take your foot off the gas, and let the engine do the work to help slow you down. You'll see the tachometer showing RPMs, but fuel flow is minimal or even cut off, thanks to our friend the ECU.
I'm not exactly sure how it worked in practice, but if it's anything like simple aircraft engines with carbs, there's a mixture control that you'd use in addition to the throttle to control air intake.