Well for me, what you fill your mind with is what you are going to think about. Christ said:
Matthew 6:22 The light of the body is the eye: if therefore thine eye be single, thy whole body shall be full of light.
Matthew 6:23 But if thine eye be evil, thy whole body shall be full of darkness. If therefore the light that is in thee be darkness, how great is that darkness!
Christians today have to be really careful with what they fill their minds with. This age is going to get worse and worse.
Now considering that this seems to be a singleplayer game, I'm not sure what a true Christian's reason for playing it would be. Using violence for entertainment dumbs down ourselves to the idea of it.
Although violence can be a necessary thing to do in a game in order to progress to reach out to others. We should not be using it as an excuse.
Psalms 11:5 The LORD trieth the righteous: but the wicked and him that loveth violence his soul hateth.