JMHO but: I don't believe there is anything in the ASSRA rules that forbids 1-piece stocks as long as it meets the other requirements. ( Although If I wanted to win many center-fire bench-shooting matches at Etna Green I might be lobbying for such

) Other single shot groups may have their own take on it.
As you can see from the final line of the rule you quoted; while "The Founders" were more interested in the traditional Euro-American-style single shot rifles. They specifically did not rule OUT the International Free Rifle-type rifles based on stock design as long as they met the other requirements--single shot, shooting plain-based lead bullets etc. (And even that
I suspect was more of an aesthetic reaction to the shiny aluminum adjustable butt-hooks that anything more substantive)
While they don't have the lines of the rifles many of us think of as traditional single shots; if I remember correctly that type of stock is original with that rifle and others of that era in Germany.
The ONLY area I can see where you might get some quibbling might be IF you were to enter your scores in the
traditional class (w/ era appropriate sights) and even that is a matter of self-identification and local interpretation.
Looks like a really nice legal rifle to me. But to be certain consult your own local schuetzenmeister since he interprets the rules at your range
Shoot it well and with pleasure.