Why would a pilot pick this military airport as an emergency landing airport?
Emergency landings often dictate landing at the safest airport, not necessarily the closest one. As I said in the comments, the flight was operating IFR and had turned the window heater on presumably for anti-ice. It could be that a line of weather was preventing VFR operation at closer airports and they diverted to the closest possible VFR airport.

When encountering an emergency there are things you don't want to do. You don't want to panic to get the aircraft down if the aircraft is perfectly flyable. You don't want to make major configuration changes, especially multiple ones, quickly. Pilots are taught to "Aviate, Navigate, Communicate" in that order. As a pilot you should prioritize flying the plane, work the problem, and determine the safest place to put down.

It is possible in this case that they could have continued IFR, but if they encountered icing below the missed approach point they would have been put in a situation with icing and no visual references.

It is also possible that the pilots recognized that some electrical problem was at fault, and even without icing conditions they would want to remain VFR because they didn't trust the electrical system would continue to function throughout the IFR approach and landing.