The design is generally called a jaeger, i.e. a hunting rifle designed for carrying while actively hunting game. The thumb trigger is curious, I have never seen one like it, although I have seen thumb triggers on other German rifles. And yes, "Teutonic" is the descriptive word for that one. Beautiful!
FWIW, 10.75X60Rmm is indeed a version of the 11mm Mauser. There were two loadings, one for the 1871 rifle (11.15X60Rmm), the other for the 71/84 rifle (which had deeper rifling, hence the smaller bore diameter), with slightly higher pressure and a paper patched bullet (very similar to our own 45-70 loadings in 405 and 500 gr versions). The 11X60Rmm was a very well respected cartridge in its day, and was even loaded in a rimless version after the advent of smokeless powder repeaters. Ballistics are close to 45-70 ballistics, being a 44 caliber 385 gr bullet over 60+/- gr of BP launching at about 1,400 fps (slightly slower in the older version). I shot my 11X60Rmm 1871 rifle for several years, loading it with paper-patched cast 350 gr .429" bullets (designed for 444 Marlin) over 60 gr of BP. Very satisfactory.