There is supposedly no longer any need to "secure" p2p distributed ledgers using Proof of Work.
I think it is more fair to say that broader definitions of "work" are being found applicable. Even Proof of Stake is just a sort of "weakened constraint" PoW.
The main problem with this, as I see it, is still the reliance on a central server for the game environment. Even with a server (or servers) operating over authenticated structures (so we could know that the OT ledger it offers is valid and that the server isn't cheating) we still rely on those servers' availability. In order to be able to sustain itself, the currency network should be independent of the participation lifespan of any given set of participants.
However any game people like to play on their phones could also be used, players who do well at the game being issued more of the coins than players who fail at the game or do not do well at the game.
The human mine-able currencies HUC and MOTO are proving that this is only a partially obtainable goal. In both cases (and really with any online game) bots are, of course, a significant influence on the game.
In the case of a network also secured by proof-of-play(/"proof-of-thought") it is also necessary to have these bots to secure the network, otherwise the transaction processing would be at the whim of the most skilled participants creating a sort of built in centralization problem.
