The check came in a post-play scrum where Backes was surrounded by three Wild players including Peters. It came in apparent retaliation for a Backes hit a moment earlier.
Peters only receives one game for the cross check to the side of Backes' head because not all of Shanny's naughty checklist was met. Backes didn't suffer any apparent injuries as a result and Peters doesn't have a disciplinary history to speak of. So the punishment is just one game.
I think this ruling carries a little bit of a hidden significance, however. It serves as a reminder that the NHL is looking at every game and every play with an eye out for these things. This wasn't a well-publicized incident at all. In fact, when it the suspension came down, I didn't even know what it was about.
In that way it is a small sign that they are serious in Shanny's offices, if that was even in question in the first place.