As the front base of the snap-on scope mount is dovetailed into the receiver ring at the same spot where the model designation is usually, I suspect it to be a M1908. The current owner merely thinks it to be a M1910. The M1908 came from the factory in 8x56 M-S aka 8mm Norm, while all M1910s were in 9.5x57. Seen from the outside only, like in the photos, Ms 1905, 1908 and 1910s are indistinguishable. Well, M1910s are in higher demand than M1908s.
These snap-on mounts and Kahles Heliavier scopes were offered as factory options in the 1930s. The leg of the rear mount ring is usually marked with the rifle's serial number. Pre-war Mannlicher-Schoenauers still with their original scopes are quite rare.