American Civil War would be my first instinct here, but then the Uniforms in art for the Boxer and Spanish-American conflicts look more like products of the 20th century... might be because the iconic oval "US" belt buckles aren't there, the jackets are longer four-pocket designs, and some of the gear is newer than what would have been carried or worn in th ACW - and I'm sure it's not just the transition from blue to khaki or olive drab colours:
Those campaign or slouch hats, though, are more like the sort of thing you'd expect to see in an ACW set alongside the iconic kepi caps..
Not that the dough boys would be a perfect match, either - the cartridge pouches, backpacks, gas masks, webbing, badges and insignia, and so on are certainly going to be a different animal, and ou'll no doubt be forced to handwave the Springfield 1903 rifles that a dough boys set would ifeature (not too hard, given how similar so many of those old bolt-action classics are to each other at that scale!) If enough of those bits are optional parts, though - Iwas very happy to see that things like gas mask bags and so on were separate bits, and that lots of head options were included, in WA's British, French, German, and Italian kits o allow a "close enough" margin of error across a couple decades from the turn of the century, into WWII, and hope the Americans are as flexible as possible within the historical limitations!
EDIT: Of course, I can't discount the possibility that I'm dealing with badly-attributed image search results, but I don't think it changes a whole lot, in a world where we just don't have a lot of choices for these wars: either make do with what's available locally, import something only a little closer, or hold breath and wait for something perfect that likely will never materialize!
Even as is, I could easily accept either modified ACW or dough-boy figures here, especially given that it's unlikely we'd see many hard plastic boxed sets for the conflicts in this transitional period between the ACW and WWI, unless it's aimed toward Wild West games, or perhaps Victorian sci-fi and steampunk..
And I, for one, could certainly appreciate and use bits like the overseas caps, campaign and slouch hats, the wefully under-represented trench shotguns and trench knives, sabres, binoculars, and flare guns (not to mention more obvious uncommon bits like Thompsons, BARs, pistols, grenades, heavy machine guns, etc.) Some of this stuff is probablybetter left to a "command and heavy weapon" kit, but either way, it's useful stuff to have around!