Liam O'Flaherty seems to intend for readers to take the phrase literally. He sets "The Sniper" in war-torn Ireland which was/is not unlike the civil war that the United States experienced. One often hears that the American Civil War pitted brother against brother, and O'Flaherty transfers that same horrible truth to the Irish Civil War which actually presented even more of a risk that blood brothers would choose opposite sides of the war. Because the Irish conflict between the IRA and Free Staters resulted more from political ideology than from two huge regions facing off against each other (i.e., the American Civil War), it is highly likely that relatives would find themselves disagreeing with one another.
Similarly, from a literary standpoint, it makes more sense for the dead sniper to be the protagonist's literal brother. If the deceased were simply killed as a result of friendly fire, it would be dramatic, but the final scene would not carry the same surprise and mood as it does when readers discover that the sniper has stalked, shot, and killed his own flesh and blood.
I think that you can say that they are brothers in a couple of different ways. I do not think that there is any evidence in the text to say that one or the other of these is wrong or right, though.
I have always taken this literally. I believe that the enemy sniper was the actual brother of the sniper from whose point of view this story is told. I am just taking this from the literal words of the last line.
However, you can also argue that the word brother is metaphorical. After all, these two guys are doing the exact same job, just on different sides of the conflict. It is said that soldiers on opposite sides of wars have more in common with each other than with their own people who have not been in combat. You can say that this is what is going on with these two snipers -- they are brothers because they are both in the same role.
I tend to believe that they really are brothers. I say this because I think a major point of this story is that these conflicts are needlessly turning people against each other when they really are similar people. Having the two be brothers is a way of dramatizing this dynamic.