I've had my horn for a while (and it works fine) but since I've gotten it I've wondered... where are the rotary strings? It's from Russia and looks very old so maybe that has something to do with it, but there are no strings, the valves are more similar to that of a trumpet. Anyone seen this, knows why that is, if it matters, etc...?

We'd need to know the maker and have some pictures at least to have an idea. There were single horns made with pistons throughout the world, but in most places that stopped decades, if not nearly a century ago. Some piston valve horns can retain their value, but most are now just curiosities.