Why was the protagonist so curious about the other sniper? Why did he go out into the street to look at him?

The sniper went to look at the enemy sniper because the protagonist sniper thought that he might know the enemy sniper.  

The reason that the protagonist might actually know the enemy sniper is because Ireland is currently involved in a civil war.  This means that the country is divided.  

Republicans and Free Staters were waging civil war.

A civil war will not only polarize the civilian population, but it will also polarize and likely split the armed forces.  Certain soldiers and leaders will fight for one side of the conflict, and others will fight for the other side of the conflict.  It is possible that the protagonist sniper was in the same unit as the enemy sniper.  Readers are told that the sniper believes his enemy to be a good shot, which he respects.  The text says that the sniper is curious about the man's identity because the two might know each other, but I also think he went to look at the body out of respect for the dead.  He wants to put a face with the enemy whose skill he respects.  

When the sniper reached the laneway on the street level, he felt a sudden curiosity as to the identity of the enemy sniper whom he had killed. He decided that he was a good shot, whoever he was. He wondered did he know him. Perhaps he had been in his own company before the split in the army.