Assuming a driver shifts following all best practices applicable to shifting with the factory shifter, will using an aftermarket short throw shifter cause any damage to the transmission?
If a driver is using the shifter correctly, then no ... there should be no difference in wear one from the other. For a short throw shifter to become "short throw", the manufacturer changes the fulcrum point of the shifter from a stock location to a point higher above the shifting point. This makes the length of the shifter below the fulcrum longer and the length above to be shorter. This means to move the lower portion further, it takes less motion above. It is simple mechanical advantage. All else being the same, it should do nothing to create more wear/tear on the transmission.