Independent Greece has only slowly acquired autonomy over its 'natural' territory. The islands of the Dodecanese, including Astypalaia, did not come under Greece governance until after WW2.
The island chain was controlled by Italy, and so WW2 in the Aegean intimately involved Italy as well as Germany. Italy was sometimes an enemy, and sometimes a buffer against the Nazis.
In the northeast part of the island is this set of buildings left over from an Italian base dating to WW2.
I'm glad in a way that no one has tried to 'restore' these buildings. Their decay is part of the story - so you know that they had a history and that time has passed.
The major WWII action in the Aegean occurred to the east on Leros and related islands, but there was spillover to Astypalaia. German survivors of a ship sinking came ashore, UK and German forces were also on the island in addition to the Italians. Have found very little info on the details and probably everyone on the island who was in WWII is gone now.
It's always useful to remember that war is fought by young men who would probably rather be playing sports and enjoying life.
The site does seem to have been 'repurposed' as there were signs some enterprising farmer is using it as a shelter for his goat herd.