Wow, that is remote.
However, the scuba diving there and around nearby islands is spectacular. If you are into diving and can handle the isolation, it's effectively a paid vacation. Check out some of the pictures here:
Google image search for "Kwajalein diving"
Shipwreck diving is pretty common. But, on Kwajalein, they have airplane wreck diving:
That's a Japanese Zero.
I just figured out the question was about working online rather than finding work online.
I remember him telling me that it was on a military base but the job was for a contractor, one of the big ones like Ratheon tho that may not have been the one.
He was not into scuba but he did say they had good recreation facilities, mainly because of the isolation.
Cool site. Btw, I think that’s actually a Douglas SBD Dauntless dive bomber in the picture. The circular cutouts in the dive brakes are a dead giveaway.