If you set the display to show the power-flow diagram you can see if the engine is delivering power or not. I don't know if this necessarily tells you whether it's running or not. Maybe it's idling and not delivering power. But it does not require any modifications to the car.
Similarly, if the instantaneous mileage shows 99.9 mpg, it's probably not running.
It's pretty cool to be cruising along a thoroughfare at 35 mph and see 100 mpg on the bar graph, or see all the power coming from the battery.
I'm going to take a guess here: Toyota chose not to include all these indicators because they want you to just drive it! The computer decides what's best for the situation, and although careful tweaking of your driving style can net you increased mileage, Toyota is aiming for transparency.
Having said that, I think an ICE-on/ICE-off indicator would be cool.