Are there any popular community games which are using Monero as money for its economy?
Not explicitly, no.
The closest example would be CryptoKingdom. They use their own in-game currency, but I believe it's directly proportional to Monero supply and/or is easy to cash out with and transform into Monero.
Probably not exactly what you're looking for, but there's also monerodice.net where users can play dice and chat. Similarly there is the tippero bot on freenode in #monero and #tippero channels where users can play dice or blackjack with Monero.