There are ways to date the age of the underground maze of buildings, although they may not have all been built at the same time.
My thoughts are that, depending on the age, it could have originally been built to: 1) support either the Underground Railroad free slave movement, 2) or as a very sophisticated alcohol distribution/ warehousing probably by organized crime in another state, or 3) something connected to Leavenworth Prison and its inmates.
( I don't know the true and correct name of the prison, sorry- but I know there is an infamous prison of long duration there. )
OR, maybe it started out as freed slave temporary quarters, was used later in Prohibition by the mafia, and also has ties to the prison. It is quite large, covering many city blocks, according to the reporter, so maybe it had multiple uses for different periods of US history.
I don't think storm shelters come into play with this for several reasons. I don't see any need for many separate buildings with separate walls and doors, etc if it was for a storm shelter. In the 1960's and before, the government plans as all were taught by the Civil Defense designated one large common area as a storm ( or nuclear fallout) shelter for a geographical region. Not many small buildings with numbered doors.
One thing I noticed was that electricity was present and a bare lightbulb was lit. Unless this was contamination of the original scene by the TV production crew or sightseering tours, which I doubt, again, I don't think the purpose was storm shelters, since the electricity usually goes off before the storm hits. Also, there should have been signs of old gov't issue first aid kits from the old USA Civil Defense, blankets, cots, emergency rations if the function was to provide short term housing from an approaching tornado.
I think it was constructed long ago, possibly with buildings added at some point after electricity was prevalent due to need, and that MANY people know or knew exactly what it was used for. People talk, and pass info down from generation to generation. People know. They just aren't talking yet.
I think this has the potential to be an interesting bit of folk history.