Can I replace a window in a garage gable wall without adding a modern header?
A ridge board (as you've drawn it) isn't a beam. It's just a connection point and lateral bracing for the rafters, and (in the case of the overhang) support for the fly rafter. There's virtually no roof load transfer through the gable wall as the rafters and wall plates, which act as rafter ties, work as a truss system, just as they do in the middle of the building.

That said, modern standards would have at least a superficial header over the window to prevent sag in the wall. It's unlikely to be a problem if it hasn't already been, as the sheathing is acting as a shear beam, but since you're modifying the opening you'll probably put in a 2x6 or better U-header to meet modern standards. 

Talk with your inspector. Even if (s)he calls for a 2x10 header, the cost is fairly minor, so it's worth doing right.