I have to go with "I don't know", using myself as a specimen.
I'm probably an unusual gamer in the way that I approach games. Most people play games completely divorced from reality, in the sense that you have no qualms in doing anything in a game because the results of your mayhem are temporary and affect only the game word which you can turn off at any time. I choose to play most games from a truly immersive perspective, where I mirror ingame what I would have done in real life.
I almost always play good karma, paragon, generally a moral and righteous person. I find that in games with resources (Fallout 3, Fable 2) I tend to be more optimistic and charitable when my needs are met. With games that offer power, (Mass Effect, Bioshock) I shy away from abusing that power once I have enough strength to ensure my own survival. With games that encourage discretion (Alpha Protocol), if my skills allow to determine if I have to kill a guard or just knock them out I tend to put in the extra effort not to shoot them in the face.
Then there's the gray areas of morality that crop up in some titles. In Fable 2, during the childhood age I was asked to retrieve a drunkard's bottle of wine that had been stolen from him. His wife said he had a drinking problem, and offered me the same reward to give her the bottle instead. I gave the bottle to the drunk because it was not my business to mettle with his life decisions, and the bottle was his because he paid for it. Somehow, that was considered a "bad action" and gave me evil points for it. When playing through Fallout 3, I encountered the Apostles of the Holy Light who were intentionally converting people to irradiate themselves into ghouls. The typical good karma response would be to tolerate their beliefs, but I choose to kill them all rather than risk more people believing that self destructive nonsense. If I remember correctly, they gave me bad karma for that too.
However, a strange thing occurs when consequences are removed from my actions. When playing Morrowind, after obtaining the ring that turns you into a werewolf I would often use the ring and cause a murderous rampage in Vivec killing many harmless guards. When the rings effect wore off and I was once again humanoid, I could stroll around Vivec immune from reprisal for last night's atrocity. Same thing happens in Assassin's creed. Once I became skilled enough to easily kill guards and then go about my business, I didn't show the same restraint as I did with Alpha Protocol. Rather than sneaking past archers on the roof, I would just push them off the building without a second thought. The archer is now dead, and will never come back just because I couldn't be bothered to walk along the street instead of roof hopping. His death will typically go unanswered because there were no witnesses. It would appear that once the consequences of murder are trivial, the value of human life is severely degraded.
So am I a moral person inside and outside a video game? I can't tell. How we treat fantasy and how we treat reality is such a nebulous subject to glean any objective truth from.