There's no way of telling if that rifle was a real WWI sniper, unless there are visible stamps to at show it was military property.
A lot of rifles during the period were ordered by commercial distributors and even small gunshops to cusomize. They were bought in all configurations, from receivers only to complete milspec configuration.
When WWI broke out, the militaries of the time were not really set up with specific, scoped, sniper rifles.
A lot of the rifles that were used for sniping, by what they termed snipers of the day and only wore their issued iron sights, dependent on the eyes of the shooter, as well as his ability to judge windage and elevation under different circumstances. You can find way more info by doing a search or reading several of the great books on the subject.
When relatively reliable scopes became available, they weren't "reliable enough" or usable under low light conditions, so they almost all were set up in Detachable Mount systems. Some of them beautifully crafted and mostly very serviceable and would hold a close to zero position when returned to their bases.
I've owned similar rifles to that in your pics, only one of them had stamps that would indicate it was intended for martial use. I traded it for a half dozen M1 Garands in VG condition.
The best I can say about that rifle is that it may have been built as a military sniping rifle, using commercially available components
One thing to remember, requirements for accuracy during that period weren't nearly as tight as they are now and I've never read about the snipers of the time training to shoot distances out to one kilometer+ other than as nuisance enhancers.
As for the stock ''customizing'' It looks like whomever did it had issues with eye dominance, which some people are under the impression is a recent thing.
Many folks just can't train themselves to shoot with their right eye, even though they're right handed.
IMHO that stock was ''modified'' to accomodate a left eye dominant, right handed individual.
I also believe that the rear Lange sight was taken off and the stabilizing bar was lost.
This is just IMHO of course.
It's always fun to try to hear the siren's calls on those old girls.
If it were mine, It would be left as is and made into a wall hanger.
You can just about bet the interior is almost as nice as the exterior.
Much more interesting as is, than cleaned up and sanded down.
