SchwarzStock posted a link to the rifle in the pic below.  I've seen that buttplate on a couple of Swiss Martini free rifles but they were in 7.5 Swiss.  I don't think the 8.15 would be competitive against the usual free rifle cartridges.

It does look like it would be a lot of fun in an open class iron sight schuetzen match.   

What kind(s) of matches would this be built for?

Oh, I'm not discounting the value of the 8.15 as a target cartridge.  I just don't think it could hold its own against the rounds for the more modern free rifles I've seen, ones like 6.5 Swede, the aforementioned 7.5x55 Swiss, .30-06 and .300 H&H.

Especially when you put the targets at 300 yards.

This rifle looks purpose built.  I'd just like a better sense of what that purpose was.

I suspect it was built for Feuerstutzen competition by someone that wanted to comply with the rules but do a bit of "gamesmanship". The only thing I am unsure of being legal is the "Gehman type" rear diopter sight...

Although this does not look very period for Feuerstutzen I think it would pass a technical inspection. Might not make the other shooters too happy. That said, I like to shoot a Shiloh Business 45 in matches here with 500gr bullets and a full charge of BP. Many don't like that either because of the noise and smoke disturbing them.

Trachten (Tradition clothing) is a part of Schuetzen so I usually wear jeans, Cotton button-down shirt, Levi jacket and Mule-Hide boots from Champion on El Paso when shooting the Sharps. Thought about using my 50-70 roller but it has a Combination rear sight on it while the Shiloh has an MVA Mid-range with an adjustable diopter that provides a much better sight picture.

We used that style of hook buttplate when shooting the German Ring match here in SouthAustralia, Started in 1864, went from BP firearms to modern single shot bolt actions, ie 300 metre free rifles. We shot the match either sitting on a box resting the barrel against a post, it could also be shot prone. Combined with a sling the hook helped to support the sometimes very heavy barrelled outfits. The X ring in the match is 2” @ 200 mts. Aperture sights only. Cheers Mal in au.

sold for about $190!