Hiya!
Great looking bike. Welcome!
Actually, you have a dérailleur. You can get rid of the idler completely. Just adjust the length of the chain from the motor so that when you adjust the wheel it is the correct tightness. The dérailleur will take up the slack on the pedal side.
That only works when the rear wheel dropouts are sideways and not straight up and down like his appear to be. With no front to back movement of the wheel he can't do it like that.