A counter argument is that Mauchly was actually interesting in using computers for weather modeling and I’m sure that influenced the design of ENIAC. He could only get ENIAC funded if it was valuable to the war effort. I’ve read quite a lot about that machine and I’m not aware of any architectural features that were specific to ballistics calculations. This is unlike the British Colossus, another early computer, which was specifically designed for code breaking and wasn’t general purpose.

As for the objection that it wasn’t stored program, I was interested to learn that it was converted to stored program operation after only two years or so of operation, using the constant table switches as the program store. But the Manchester Baby, which used the same memory for code and data was more significant in the history of stored program machines.

On the general question of “first computer”, I think the answer is whatever machine you want it to be if you heap enough conditional adjectives on it.