I've just discovered this page on k.u.k. mountain troops on the website of Bekleidungsamt XIII.
These guys are armed with the Steyr-Mannlicher M95 Stutzen (a shortened version of the M95 rifle)... (note the rifle slings!)
...and in this here German-language video (at around 15:50) ther presenter mentions that the mountain troops used a special rifle sling, that was easier to adjust in length, which is what I assume is visible in your original photo and on the reenactor's page.
Thank you Karl, the reenactor photos clearly show that the buckle was used at both ends as a means of attaching the sling to the rifle. The video further shows the buckle detail - great stuff!
Nap many thanks for those book scans, specially the close ups which will further aid in the details. I had estimated the rifle sling to be about 40mm wide after scaling the photo so the proficiency badge fit in a 45mm circle, and you helped confirm that.