First off, you've put this in the wrong forum, it's really more Land and Leute, no? And it's a pretty trollish question (Nazi comparisons in the first post, doesn't take long to get to what's-his-name's law ...), but nevertheless ...
I'm not familiar with the details of the case beyond just what I've seen in the news, but there may have been some extenuating circumstances. If the soldier confessed fully and agreed to help with the investigation, that could have justified a reduced sentence. If he claimed he was in fear of his life from Iraqi civilians in general, that could have counted as self-defense, another mitigating factor. If he had never committed any previous crimes, his sentence would generally also be lighter.
That the whole thing took place in a military court probably also means that there were different rules of evidence as well as different priorities. The sentencing officers have to take into account that their greatest practical need is for soldiers who can return to combat, especially at a time when they desperately need more troops. If they send him back to risk his life later, it's more useful to the army overall than just keeping him locked up.
And there's the question of how high up he was in the hierarchy. I'm not familiar with the names you mention, but my impression is that most of the Nazis who were hunted down decades afterwards were responsible for far more than one or two deaths. They may not have killed many people with their own hands, but they were in a position to give orders that resulted in the deaths of hundreds or thousands.
All that said, I do find it discouraging that no higher-ranking American officers or Pentagon officials have been held to account for the policies that made Abu Ghraib and Guantánamo possible. That seems to me a much clearer miscarriage of justice, or at least, a failure of ethics. At least this guy was tried and found guilty, even if only as a scapegoat for decisions and attitudes whose real cause was far higher up the chain of command.
But in a state bound by the rule of law, what counts is the letter of the law, not its spirit. If lawyers find loopholes that let guilty people go free, the solution is supposed to be to (elect people who will) write better laws. And as a general principle, it's better for the occasional guilty person to go free than for an innocent person to be punished. Of course that also happens sometimes, but the loopholes often exist because the laws are written to err on the side of the presumption of innocence. We wouldn't want it the other way around -- that would really be a totalitarian state, which, for all its many flaws, the US is not.