This is the first hint we get in the poem that our speaker is talking about war. And it's not like he was up in an airplane, or working as a medic in some hospital tent. The guy was on the front lines, facing down men who probably looked a lot like him.
And staring face to face, (6)
At this point, we can probably see what's coming. He's staring down his supposed enemy, who—we know from the first stanza—could just have easily been his bestie. It's only a matter of time before this meeting comes to an end.
"I shot him dead because— Because he was my foe, (9-10)
The hesitation, the repetition—they tell us that this dude doesn't quite buy what he's about to sell. He tells his listener that he shot the guy opposite on the battlefield because the guy was his foe. But isn't that begging the question? We mean, who says he was his foe? And why?
"Yes; quaint and curious war is! (17)
Remember, these are the speaker's words—not Hardy's. If he were talking here, he'd probably say something like, "Awful and atrocious war is!" Or "Heinous and pointless war is!" Still, though he's using these quirky words—we get the picture. War is not quaint and curious. It's cruel and capricious, thank you very much.