In a forum I correspond to, one guy is asking about that gun, declaring it is a "target gun, fitted with peep sight".
Does anybody know such a weapon?

Not much information to go on. What forum, photos?

MS 1903 with a flip up peep on the stock maybe?

Might have the model and caliber wrong. Mod 92 Steyr in 6.5x53R were after used/converted to 303 British for long range “match rifle” shooting at Bisley to 1200 yards, from a back position. Aperture sights were mounted to the top of the butt, just ahead of the buttplate, with an aperture/ Galilean foresight used.

The English makers sometimes tarted up old Greek Mannlicher Schoenauers. I have seen one by someone that still had a knob but not the usual cherry-plum monster with hole. It looked more like the smaller, bent-over handle of a Steyr military model made from 1930.