On several levels of the internet they all try to get a foot in:
1. Cloud: AWS, iCloud, Azure, Gdrive & App engine - Facebook hasn't got a storage or computation sollution
2. Social: Google+, Windows Live, Facebook - Amazon and Apple don't have real social networks
3. App stores: Apple app store, Play, Market Place, Amazon Appstore - Facebook doesn't have a real app store.
4. Operating system: OS X and iOS, Android, Windows - Facebook and Amazon don't have a OS yet.
5. Browser: Internet Explorer, Chrome, Safari, Amazon Silk - Facebook doesn't have a browser yet.
I really think that all companies will battle each other on all the levels because loosing one level will cause the collapse of the others.
So, Facebook definitely needs a browser.