It takes millions of pounds and several years to develop military systems. The computers running the systems (everything from heating/cooling, to engine management) are integral parts of these systems, and explicitly configured to do these specific tasks. These task-orientated units would have be designed down to the nth degree, complete with extensive operating/troubleshooting manuals and config guides, including approved 'gold images' to rebuild them easily if required. Swapping out the base OS needlessly (if it's still capable of performing its duties) would require an extensive rebuild of the system concerned, again taking years to get through all the admin, testing, and sign off hoops.

I very much doubt when it says 'running XP' it means the general purpose computers for end-users to use.

Obviously, if these XP machines are not air-gapped, or behind hardware firewalls (with very restrictive rulesets) away from the general internet, then that's insane. Cynical as I am, I still have a hard time believing that these XP machines would be remotely accessible from outside the ship in question.

Edit: I've zoomed in on the image in question. Yes that's a Windows XP lock screen (the header of the dialog is blue, if it was Windows Server 2003, it'd be grey) However it's in 'classic theme' mode. As it's on the lock screen, then that's a 'system wide' setting, which infers that the themes service is disabled. If they've disabled the themes service, then it's safe to assume that lots of other parts have been disabled or locked down also. This doesn't make XP safe, but it does at least a) mitigate the risk somewhat, and b) indicate that steps have been taken to secure the OS.