The most common and widely used meaning of the word theatre is (from The Free Dictionary):
a building designed for the performance of plays, operas, etc
Why then can it also mean (as one of its other meanings):
a major area of military activity
(as in "the European theatre of WW2")
War is in no way an act or performance (performing surgery in an operating theatre still fits) so why is "theatre" used in a military sense?
The etymology is:
from Latin theātrum, from Greek theatron place for viewing, from theasthai to look at; related to Greek thauma miracle
This fits the performance theatre definition but does not help with the military meaning.