First killer app was calculating trajectories for artillery.
For example, the Mark I mechanical computer[1] could, when pointed at a target, measure its distance, altitude and heading, its own ship's speed, pitch, and heading, current windspeed - and combine that with the chosen projectile type, weight, propellant type, and current temperature - all to compute a firing solution that had the best chance of sinking ships adorned with swastikas, or a rising sun.
Not a general-purpose computation machine, but work on these sorts of devices heavily overlapped with work on programmable computers.
[1] https://en.wikipedia.org/wiki/Mark_I_Fire_Control_Computer