Why is this case being tried in a court-martial?

Two women, one a lance corporal in the New Zealand Defence Force and the other a civilian, travel to New Caledonia on vacation. The lance corporal is said to have assaulted the civilian because of jealousy over a man. Beer had been consumed. Details here. Excerpt:

Military police Corporal Delia-Ana Meszaros said she received a phone call at the Trentham Military police station from the complainant after she had returned from holiday. 

She said the complainant told her she had been assaulted while on holiday in New Caledonia by a service person. 

"She said she was a civilian, so I had to talk to [someone] in regards to jurisdiction issues." 

Meszaros said this was because in cases that involved civilians they usually passed them on to the New Zealand police.  

"[However] he said because the case happened outside of New Zealand, New Zealand police could not deal with this case." 

This meant military police investigated.

Queries: Should this case be in a military court? Would a New Zealand civilian court have been able to try it if the defendant had been a civilian? If not, why the difference? Are there no courts in New Caledonia? (There of course are, mais on parle français and French criminal law applies.) Cf. Re Colonel Aird; Ex parte Alpert, (2004) 209 ALR 311, [2004] HCA 44, discussed here.