There is a miss-conception that Pastors by definition are not people but rather a walking pulpit. This conception would be built upon many factors:
Experience of person,
Experience of influential people around said person,
Culture of person,
Conceptions of religion, God and religious leaders.
I would put the idea forward that our experiences shape our beliefs and such that we define all experiences by beliefs. It's a cycle.
That is how one would come to that idea.
---------------------------------------------------------------------------------------------
To have an understanding that God is some idea 'X' it would be logical to define all elements of God as containing or utilising 'X'.
Example if God is perceived as being a 'hater of evil', then it would be expected that those who preach God's message would display this element of God and 'hate evil'.
So bringing this point to the video game world, we see that there are some who would perceive that God is love. Love does not hurt or kill, therefore any killing is wrong, therefore a pastor should not kill even vicariously.
What the limitation of this way of thinking doesn't understand is that video games by design are a contextualised situation. A story. And that is what matters. If you saw two people fighting in the street it's a blank context and a person might say that is outright wrong. But if it was know that one man was trying to rob a lady and the other man was stopping him, then the situation has a morality and even heroic cause to it. Where rather omission to the situation would be the more evil of deeds.
Working the idea of context back to Christianity and it's message.
Christianity is about Jesus Christ and His message. Salvation is by Christ alone, believing in Him and His grace, that brings one to God. It is not earned but rather a gift freely given.
Christ brings humanity who cannot earn salvation, but rather in grace by sacrificial atonement brings all humanity and creation to the place of restoration, when one chooses Him. Therefore salvation is about restoration of God into the believer's life. To make right what the enemy has made wrong.
The last point to add is the desire at the heart of man. This is the call to adventure, the desire to be a hero, to rescue a beauty to do great things, to make a difference, to be a man.
Taking the idea of contextualised situation, the Christian message of redemption, and man's desire for adventure we can arrive at video games. (within reason)
Video games like Doom are about restoring order and justice, about removing the evil horde of minions. Games like Call of Duty, medal of Honour, are about restoring freedom to the oppression of the the evil Nazis. Games like Mass Effect area about restoring and saving.
Video games set a situation where something is wrong and a battle needs to be fought, an adventure taken or a Princess needs to be rescued. This speaks to man's heart and even to the idea of redemption. Video games have a way of speaking to a man's desires and that is most likely why males game. The sense of adventure and the ability to achieve.
To conclude I would reason that all conceptions come from belief, belief comes from experience. That would see how this conception of pastors as non-gamers would arise. But I would debate that the Christian message is about restoration (and relationship) and as such video games offer a world to be restored. And as such the need creates a battle to be fought and that is at the heart's desire of man.
While there are a few non-desirable elements in games, like swearing, it's up to Pastors and Christians to really read the Bible and ask God, whether these elements make it a no player. I would rather put forward that too many young men play video games and waste their time on the internet, then actually live life. It's all about balance.
Yes I am a Christian and a Theology student.
Cheers