What is this part? Any chance it's not crucial?

Yes it is crucial, but it is repairable. It needs to be re-soldered into position on its contacts, but the orientation is also important, it must go back on in the same way it was before it came off. Look at the other similar part (just to the left in the picture) and see if it has any markings on it that orient the part. It may also be possible to see the orientation from looking at the part that fell off, look at the bottom contacts and see if there is any way the solder break(s) look like they fit the contact points on the motherboard contacts. You may be able to tell just by trying to re-fit the part onto it's contacts and see if there's only one way it fits into the broken solder points properly.

Good luck, and be careful about static, use anti-static measures whenever you work with electronic parts.