The orientation of the cylinders really is not important. The check valves allow the cylinders to remain in phase, or lets them return to phase at the end of the stroke in either direction. I'd consider them necessary for implementation, but not function. Without the CVs, you'd be breaking fittings to bleed, fighting to regain any lost timing, fighting to achieve synchronization at end of stroke, etc. The CVs allow bypass flow around the piston when the cylinder is at the end of the stroke, letting the other cylinder travel to the end of its stroke when they are out of time.