I am now pretty much convinced that the purported German "marine" ("Seesoldat") in the above photo is in fact a sailor ("Matrose") on some sort of shore duty or land expedition ..... which, unfortunately, means that he would be more likely to be armed with a Model 1871 rifle a lot later than would a Seesoldat .....
I found this 1880's photograph of a German Navy sailor attached to the Naval Artillery. (The full cap tally apparently read: KAISERL. MATR. ARTILLERIE", short for "Kaiserliche Matrosen Artillerie", which translates literally as "Imperial Sailors Artillery".)
Anyway, note the style of his cap, which is the same as worn by the chap with the wristlet watch. There was also this comment about his shirt: "His shirt is the blue woolen winter naval top ('Wollenes Hemd' or woolen shirt) with
removable naval collar in a lighter shade of blue with three white stripes ...." (Emphasis added by me, considering that the chap with the watch has no such collar, but his shirt certainly otherwise looks the part ....)
Marine Infantrymen (Seesoldaten), on the other hand, would have been more likely to have a "military-style uniform", with some sort of tunic, as worn by these chaps in China -
- and I gather that their headgear was noticeably different .... either a peaked cap or an un-peaked field cap, such as worn by these Seesoldaten -
I found these images on a very extensive website dealing with "German Colonial Uniforms" .... which has a great deal of information on both Seesoldaten and Matrosen, since they were also very often used in German colonies and foreign expeditions. I gather from my cursory look that the general styles of uniforms for Marine Infantry and sailors didn't change all that much through the German Imperial period (i.e. about 1870 through 1918) which doesn't help much with fixing a date for the "mystery German watchwearer". However, I barely scratched the surface there, so if anyone wants to give the site a more complete search, it is here:
http://www.germancolonialuniforms.co.uk/