The gap between the arm pad and the back on this chair is not what is left over after the arm was made. It is a measurement, and the measurement is a hand.
On a chair with arms that run the full depth to the back, the only way to push yourself up is to press down on the top of the arm with a flat palm. That works well enough while you are quick on your feet. On a chair with stub arms, there is a clear space behind the pad, and the hand can close right around the arm rail and grip it. Gripping gives far more purchase than pressing, and it is steadier.
So the arm length is set from the back of the pad forward, leaving a gap wide enough for a hand to pass through comfortably rather than just wide enough to look open. On the standard chair we work to a generous adult hand; where a client tells us the chair is for someone who needs more help rising, we widen it and lower the arm rail slightly so the grip falls where the hand naturally lands.
It reads as a style decision - the open-armed shape is a period one. It is also the reason people find this chair easy to get out of without thinking about why.