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That "military music" requires specific musical tradition in society. USSR had some kind of local scene for that music, common people often had guitars and made own songs. Genre was often called "bard song". There were tourist songs, army songs, political and criminal ones. Stylistically they were mostly similar, just guitar without complex melody, it can even be described as poetry (often bad) with music, where music isn't central thing, but lyrics is. Songs were made by different social groups, from intelligentsia to commoners, criminals and soldiers.

https://en.wikipedia.org/wiki/Bard_(Soviet_Union)
(that article is slightly shallow though)

That Afghan music wasn't some unique thing, there were military songs before and after. Now tradition mostly gone because no one knows what guitar is, and modern conscripts listen mostly to junkie rap. But there still some bands that play in that genre.

I don't really know much about musical trends of US army, but I guess they wouldn't do anything similar in 2022. US army also less connected than USSR one was, because it lacks conscription, so common citizen in USA cares less about soldiers than commoner in USSR.