Yes but this is not a half H-bridge it is just a simple high side switch and not a very good one at that. The driver circuit can't be an arduino because it does not have an open collector output. Driving a load in the source is not good because the load current backs off the gate voltage and the FET ends up operating in the liner mode. This = hot.
Actually, on the Milton Bradley Big Trak, they used a weird "half h-bridge" design with a dual ended power supply; only two transistors used per motor.
So half the batteries drive it forward and half of them backwards. It doesn't make for a very even battery usage. You end up changing them all when only half are discharged.
I looked into other designs - I found this:
Conventional enough design. It is a bit asymmetric in it's sensitivity due to the use of the transistors in the optos, one pair in common emitter and the other in common collector.
It seems safer
Can't see why you say that if all LEDs are on there is still a short through the transistors of the bridge.
Generally an NPN only bridge is less efficient (generates more heat) due to mixing common emitter and common collector drives and generally requires non overlapping drive signal to make it safe.