My first thought was it may have nothing to do with Windows 3.1 and more to do with a software package they're running. Which after I clicked on the article appears to be the case. While I'm no expert on this type of system, there may be hardware associated with the software and therefore not an easy path to upgrade to newer operating systems without upgrading the hardware too. Or they're running an ancient version of DECOR that's incompatible with newer operating systems.
Being someone that tests electronic components, this isn't an uncommon problem. I have ATE's (automated test equipment) that run on operating systems going back to Windows 98 and everything in between including one system running Solaris on an ultrasparc. Some of these don't have a path to upgrade the operating system, some do but you'll have to rewrite/rework your old code, and others just have a plain out exorbitant price to get there. ATE's are very expensive so we're not going to throw them away just to upgrade the operating system.
Having said that, you'd think that whatever overall system they're using would have been completely upgraded by now. I can't imagine these airports can't afford it..