Update: The Facebook Messenger app is now back in the Windows Store for download. Thanks to everyone for the tips!
Ironically, the app received a small update earlier this morning for users who already have Facebook Messenger installed on their smartphone. However, if the app is uninstalled the Windows Store shows that it is not available. There have been reports from some users about touch problems with the app, and it's possible Facebook removed it from the store to fix those issues.
We will post an update when and if we learn more about the Facebook Messenger app's current status.
Thanks to Olivér Aho for the tip!