As many mobile app games have shown, you don't need a cryptocurrency to achieve this, just some arbitrary point system. I think GP was asking, "Why Cryptocurrency?" since the benefits of blockchain don't really translate to this system.
Look at Paypal USD Balance. It's really just a "token" issued by PayPal, an IOU where 1 PaypalUSD = 1 USD Debt from Paypal. But PayPalUSD can only be used within Paypal.com. The only way to bring PayPalUSD outside of Paypal is to call in your debt to PayPal and withdraw the money to your bank.
PayPal has always said that their success relies on people holding PayPalUSD. People who keep their money in PayPalUSD are the ones making PayPal bank. First of all, it costs Paypal next to nothing if that user sends their PayPalUSD to another user. Yet they collect transaction fees. Furthermore, PayPal can throw this money into low-risk investments and earn 3-4% on it.
Facebook tokens are PayPalUSD 2.0. They can be used within the Facebook.com ecosystem. But on top of that, people can withdraw them and use them outside of Facebook.com. Basically, any website can start integrating these FacebookCoin. It means less people will need to cash out, and will instead keep their money in FacebookCoins.
You can convert PayPal directly into US dollars at your bank, so I don’t think they would see any benefit to supporting such a distributed token system unless the could make a cut on every transaction.
I’m having a hard time seeing Facebook being able to support a stable coin without being subject to the same regulations and cost as any other system.
Perhaps they will get a competitive advantage through data mining and could charge smaller transaction fees.
Because it's cool and everyone is doing it.