We can't really draw too many conclusions here; we don't know whether general Sīha is actually going to war. Plenty of people in the military never see an actual battlefield. I'd guess as a Sōtapanna, if it actually came to a situation where he would either have to kill or encourage killing, he would not do it.
I think we need to be careful of generalizing too much from what little background information we get from the Suttas. For example, if you look at the , it's not saying that "everyone in the entertainment industry is going to hell", but something more nuanced. The Buddha tells us exactly what conditions could lead Tālaputa to a bad rebirth: a)being intoxicated and heedless himself and b)promoting intoxication and heedlessness. So, is it the case that many actors/actresses could be promoting unskillful behaviour? Probably. But are all actors/actresses being unskillful to the extent that it leads them to a bad rebirth? I don't think we can categorically say that.
It's the same issue with the military. Is the military generally a conducive place for cultivating skillful conduct? No. But we cannot make any categorical statements and ultimately it has to be considered on a case-by-case for every individual in the military.
"Delighting in existence, O monks, are gods and men; they are attached to existence, they revel in existence. When the Dhamma for the cessation of existence is being preached to them, their minds do not leap towards it, do not get pleased with it, do not get settled in it, do not find confidence in it. That is how, monks, some lag behind."
- It. p 43