It does strike me as something like the sporting match rifles from the U.K. It was common for sportsmen to use one rifle for hunting and friendly competition.

Back to the OP, the rounded grip (Prince of Wales or "bagged" as Westley called it) seemed to be quite popular on the earlier 6.5mm Steyrs. My Fraser has a rounded grip and a good looking H&H just sold at RI which is very similar.
I suspect Steyr may have had a pattern rifle they sold to the British trade to be finished as they are all so similar other than the sighting.