Unless you use a sight system of some sort, e.g. sighting down the shaft, using the point of the arrow as a sight pin, there is no need to be concerned with matching the shooting side and dominant eye.

Cant the bow a little, keep your shooting elbow high, tuck your head into the bow and stare a hole in the spot you want to hit. Don't lift your head or you'll shoot high. I have missed 3 cake shots at deer that were...ah, very close when I lifted my head.