The 8x51 K Mauser cartridge, old name M.88H, predates the .308 Winchester by about 50 years. It was a shortened version of the 8x57 I , M.88G, to fit into the Mauser K short action. The standard load used a 196 gr jacketed bullet at about 2100 fps. These light rifles were intended for shooting roe and fallow deer, being less destructive than the contemporary 8x57 I loads. At those pre-WW1 times a German hunter had little chance to ever see a red deer, let alone a wild boar or any other larger game.
Here is a scan from the 1904 DWM catalog, showing the case besides the 8x57 I one.