Since this is a German rifle, it is likely shown as a 10.5mm rifle because it is marked as such in the proof marks, either directly in mm or in a gauge measurement that translates to 10.5mm. They were marked with the bore (not groove or bullet) as Raimey stated. The actual cartridge's nominal designation could be any one of several different ones, and not necessarily of German origin. To ID the cartridge, a chamber cast will be necessary, together with "slugging" the bore. Rechambering such a rifle is a poor choice, for several reasons, not the least of which would be the need to re-regulate it, even if it could be done safely. A much better idea would be to handload for it, even if you have to make cases and bullets from something else.
Mike