I had one of those on a .28-30 and it worked fine. As I recall mine had odd sized scope blocks. No problem now, of course, since Steve Earl can make anything you need in the way of scope blocks.

james-1,
    I've got one just like it . It's a Winchester "No. 8 ". According to Campbell"s book Volume 2 on the Winchester Single Shot, Winchester made them (or had them made) in the 1930's. Campbell supposes they were made for small-bore applications. He also says the tube was made of steel, although mine is a brass tube. I can't see any problem with it standing up to the recoil of your Stevens .25-20. It seems to be well made for the era. The screw on the outside of the tube about 2" from the back end holds the cross-hair ring in. Just make sure the screw is snug so the ring doesn't rattle around. Campbell says that 'little is known" about this scope. It seems we've got an actual rarity. Not that this makes them worth anything, it just makes them one of the odd ones. 
                                                               SteveC

I believe that was the scope that Winchester made specifically for the models 52 and 75 Winchester .22's. Since your Stevens is in .25-20, I wouldn't worrymuch about recoil regardless of the scope used. Not really a caliber that could cause recoil damage in a Stevens 45 action.