First, even if the aircraft is controlled using a yoke, the pilot is still controlling using his left hand (left hand on column, right hand on throttles/PCL). This is not much different and almost all pilots switch from controlling using their right hand to left hand pretty easily (they'll usually do this while training itself as they switch seats). The basic concept is same as say, a Boeing 737.
Boeing 737 cockpit, from gearthhacks.com
The basic control layout in airliners is that the pilot/copilot controls the yoke/sidestick with one hand and throttles/TCL (and flaps etc.) with the other hand. Having dissimilar layout for pilot/copilot has some advantages.
At the minimum, the throttles can be placed in the center. If the pilot's sidestick is to (his) right, then the throttles have to be placed in the left, resulting in duplication. This can be seen in the B1 Lancer, where the pilot's throttles are in the left (though the aircraft has a centre stick).
Image from left wingsovereurope.com
While this may be possible if only the throttles were to be duplicated, it is very difficult to do so with the whole center console.
Also, having the sidestick to the left side serves as a good hand(wrist) rest.