I'm shocked that this ended up on a commercial flight. After reading Command and Control though, I'm sure this stuff happened all the time in the past and it was just quietly swept under the rug.
It's an inert missile you can ship pretty much anything on commercial flights with a few exceptions as long as you have the proper customs authorization.
I was surprised too. It's not that it's dangerous, it's that it's potentially sensitive military technology.
According to the WSJ story[1] cited in this link, "the shipping crate was clearly marked as containing material subject to rigorous export controls". Makes me wonder how often this sort of thing gets shipped around, and how many spy agencies have people in place with the world's various freight operations.
Those rules don't apply if you actually ship cargo, as long as the cargo is secured according to regulations it can be put on board even if it's a commercial flight which carries passengers.
Even as a normal passenger you most likely can make arrangements with shipping dangerous goods with any airliner they would most likely direct you to a logistics provider that will handle it according to regulations.
I've bought quite a few dangerous goods like actual pure lithium which were shipped internationally by air using regular post (which in most cases is shipped through regular commercial flights) including actually pure lithium and various pressurized gas containers.
The shipping costs were not even more expensive than what would a normal package of the same size and weight would cost the only difference is that i had to send them signed customs forms approving the import prior to them shipping it to me.
The only other different thing is that on one of the bigger packages (a canister of helium) the local postal service actually called me and said i have to pay extra for a specialized driver with a permit to transport dangerous goods to pick it up and deliver it to me, that actually ended up costing more than the express air shipping and oddly enough only one package was flagged which just shows how poor custom enforcement is actually is unless there's Ebay or Amazon written on the invoice in which case they know exactly how much to rip you off on import taxes.