Currently, game objects are stored in centralized and closed databases, so with blockchain those objects (like currency, items, comsetics etc.) could be stored on blockchain, which is a public and distributed environment.
However, a game has to be open source to benefit from the blockchain, and be very lightweight so running a game server would be cheap. Without those two requirements blockchain loses almost all its benefits - game objects are only useful if you have access to the game, and this is usually under full control of the company who runs this game. Blockchain can be used as a proof that all in-game item are created according to the rules, i.e. the company is not creating them out of thin air to sell for money to players, but for this to work users who want to verify it have to run a full node, which can be very cumbersome if there's a high amount of transasction (not only p2p, but also events like item drops). If players are connected to the blockchain via SPV client, it's pretty much useless, because they can't verify all the rules of blockchain.