From the article: shifting into neutral and coasting when safe

Correction: on a modern EFI car, coasting in gear burns less fuel than coasting in neutral.

While coasting in neutral, the engine (more properly the ECU) burns fuel to maintain min RPMs, a la idling. By coasting in gear, the engine maintains min RPMs by using the forward motion of the wheels to drive the engine--actually burns no fuel.

The trick is to avoid stalling when the car runs out of forward momentum!

BTW a Prius is no more fuel efficient than a diesel engine in a similarly sized car. The ideal is a diesel hybrid.

You forgot the overall energy situation. Yes, your car coasting in gear is consuming less gasoline than I am coasting in neutral. However you are also losing kinetic energy from the engine drag which I am not. If you are slowing to a stop that will eventually require braking, that is fine (but in that case I am not coasting in neutral either, so you have no advantage). But otherwise I win.

As a reference point, my 2004 Audi 1.8T coasting in neutral at 40 mph is right at 200 mpg in moderate temperatures, so burning one 0.2 gal/hour. It is not zero, and I engine brake on long downhills to save it routinely. But it is nowhere near so much as the cost of getting back kinetic energy wasted in un-needed engine braking.

Assuming the opening poster is correct about EFI, which I believe he is, it saves fuel to drift in gear as long as there is enough of a downslope to prevent the car from decelerating. It also saves fuel to keep the engine in gear when a stop can be anticipated and a gradual deceleration is acceptable.

I doubt that it provides a significant benefit, but I attempt to do take advantage of this. When I am going down a long mountain decline I keep the car in the gear that is necessary to maintain approximately a constant speed. This saves brakes and cuts fuel consumption to zero. When I am coming to a stop that I can anticipate early I let the engine resistance slow the car down gradually and finally I will drift forward with the car in neutral when the car is moving to slow to keep the engine alive.