"War Game" is not a term that was widely used in the 1900's.
Search instead, with keywords like "Maneuvers", "Exercises" or even "Strategic Exercises".
Also, the Navy had it's own term for Exercises: "Fleet Problem", "Joint Fleet Problem" and the Marines used the term "Field Problem".
The most recent Fleet Problem the USN conducted, was Fleet Problem XXI (1940), Fleet Problem XXII (scheduled for 1941) was cancelled. The first Fleet Problem was conducted in 1923, denoted by the Roman Numeral I, each following year gained another Roman Numeral value.