It is interesting to note that in the Greek Ieratikon the wine is called "nama" of which there is actually a wine called Nama from Santorini: http://www.canavaroussos.gr/uk/oinopoiia.html
Nama is a style of wine - like Port or Riesling. Nama is created in the same manner as Commandaria, with a drying of the grapes to increase sugar content before pressing. Alcohol in wine is produced by conversion of sugar. A higher sugar content means more alcohol, unless the process is stopped at a certain point, that allows for sweetness.
This natural fortification and sweetness is why Nama and Commandaria are used for communion. Port has natural sweetness but the fortification is gained by turning some of the wine into brandy and then adding back into the wine.
The high alcohol content is needed so the wine will not go bad quickly, alcohol acts as a preservative.
Once last note, Nama tends to be the preference because of the ruby color and pure grape taste. There is something special about the Santorini, volcanic soil that makes the Nama from there shine in taste and color.