Assuming Steyr followed their usual practice, the date on the left rail is the manufacture date, not the model date.
The magazine rules out the M1895 and earlier rifles; it looks like the 1904 Exportmodell, which was made in 8x57j, and used the (German) Model 1888 clip. Many went to China, the Austrians themselves used them in WWI, and German arms dealers sold some 12,000 to the Ulster Volunteer Force (Protestant loyalists) in Ireland.
While Steyr concentrated on military arms, they did make sporting rifles as well. Whether that is a factory sporter or a sporterized military rifle I can't tell from those photos.
Jim