The citizens of Germany were in many cases a victim of their government the same as those who were persecuted. In Germany the state of mind during Nazi reign was survival, the soldier would have died for not being loyal to the Nazi party. That is unless he drank the Kool-Aid and was taken under Hitler's spell, in which case this question becomes a lot harder to answer.
Yes, the former Nazi guard living in the United States should be extradited to face charges of war crime, because it is never too late to effect justice in a situation like that. The Nazi guard probably didn't let his captive live, even if they were very old, so he should not be given the same courtesy by anyone else.
If he was really a Nazi guard, then he needs to face charges and punishment for his crimes. Even if he was not actually a guard, then it is important for the charges to be investigated and examined. Him going to trial could bring out more information about other individuals.
The Nazis were the perpetrators of so many atrocities during WWII, allowing any of them to avoid facing trial would be an injustice to all those who suffered at the hands of them. This man should be extradited and tried as so many of his colleagues have in the past, and punished as seen fit by the courts.
I think charging him with war crimes and sending him to prison will not change anything. The War is over, So let the old man live his final years, Think about the other U.S. soldiers who are still alive today, they too killed a lot of people, just like him, just like any other German soldiers. It doesn't mean a person is bad if he's German or part of the Nazi government, It's the same with not all Americans are bad. Plus, he's a soldier and his objective is to follow his leaders, just like any other ordinary soldiers.
The man that is currently being held as a former Nazi guard, Johann Breyer, is 89 years old. He has lived decades in this country without causing one ounce of trouble. He was more than likely part of the military of Germany for a pay check so he could survive and take care of his family. Disrupting his life now or sending him off to be prosecuted is simply a huge waste of time, money, and effot.