It's a Thermal Resistor and shouldn't really have torched like that, doesn't matter which way the replacement gets installed either.
Check your front USB ports and make sure the connector isn't damaged and causing a short. It could have just fried on it's own too, that happens sometimes, but is odd for that kind of part the way it is in the circuit, unless there is a short on the USB connector, and even then the 360 should have shut down before it fried it that bad.
It'll be fine without it, but one of the USB ports up front isn't going to work since the 5v has to go thru that part, so if ya use them it needs to be replaced, and any from any other board will work as a replacement.
Also if the board is torched make sure all of that is cleaned up before powering it back up, the nasty thing about a circuit board burning like that is it'll conduct, like a Resistor, when it's burnt up.