The feds clearly won, because if the court had upheld the ruling of the court below, which ruled that the National Firearm Act was a violation of the Second Amendment, and thus no law at all, they would have lost.
However at most the Miller ruling would mean that only keeping and bearing arms of military significance is protected by the second amendment, at least that was interpretation of "Miller" put forth a couple of years later by the First Circuit in "Cases".
What the remand may have been for, was to determine if a short barreled shotgun was a militarily significant weapon.
For a fact, they had been a few decades before, and even at the time were in use by police, as they are today. Police, more likely to be "mounted", are willing to give up ammunition capacity for "handiness", which is the reason the military prefers somewhat longer barrels, not for the barrels themselves, but for the added magazine capacity.
Why go back a few decades? Why not simply go back to a world war they just finished fighting -- WWI?
In that war, the military used 20" shotguns. Seems to me that if the barrel was less than 20", certainly if it was less tham 18", its military "significance" would be questionable.
"and even at the time were in use by police"
Did the Miller court bring up "police"? Why are you?