The strict differentiation of 8 mm I and S caliber barrels and cartridge designations came with the German 1940 proof law only. According to proofmarks and serial number your rifle was made in 1931, well before. In his book “Mauser – Original Oberndorf Sporting Rifles”, page 275, Jon Speed shows a 1926 Mauser factory dimensions chart. Here the dimensions of 8x60 barrels are given as 7.85 mm land, 8.1 mm groove, twist length 240 mm. Your barrel is slightly wider with an 8.15 mm = .321” groove diameter, sort of a compromise. But that factory chart has a footnote that reads translated: “* The barrels for the 8x57 and 8x60 get the chamber and throat for the S cartridges, so those may be used as well.” So the 1920s -30s original Mauser Oberndorf sporting rifles digest 8x60 S loads happily. Go ahead and shoot it with modern 8x60 S ammo.
The same topic was discussed here several years ago:
http://forums.nitroexpress.com/showflat.php?Cat=0&Number=231141&an=0&page=9#Post231141