The DoD even spent a ton of money building their own Iridium gateway in Hawaii, which is linked to the other DoD teleports in Hawaii. A lot of military M2M stuff uses Iridium, not just voice. Blue force trackers, etc. The current corporate incarnation of Iridium that acquired the network from the original bankrupt entity would probably be doing OK even without the military, but it's certainly doing better thanks to all the NATO countries that use Iridium stuff.
Even without the military there is a decent sized worldwide market for low-data-rate text email and voice in literally any location on the planet. Iridium works in polar ocean regions with Inmarsat doesn't. It works in fun places like the middle of a desert in Chad or southern Libya. Globalstar was at one time Iridium's closest real competitor but it was a network architecture failure, even before their first generation of satellites developed severe reliability/failure problems. Until very recently Iridium's only real competition for true 'global' coverage was Inmarsat, and Inmarsat is based on geostationary satellites so it's problematic to use at high latitudes. Inmarsat also until very recently did not have a handheld phone product, an Iridium phone was small enough to put in a backpack or small Pelican case while an Inmarsat terminal was the size and weight of a giant 17" gaming laptop.