I've been thinking about this topic some since I first posted the question ... there's some interesting responses here, and my thanks to all participating in this thread ...
A couple thoughts ... Gaming has been almost instrumental in my relationship with one particular friend, and my corresponding ability to be an effective light to him. At one point we did a lot together, having the same classes, workplace, study groups, with a good dose of gaming sessions. Then comes graduation, so all that changed, except for the gaming. I wasn't what you could call socially adept, so it took me a while to find other arenas to spend time with him ... until that happened, gaming was the kept us in touch. Many of the games were actually single player games that would provide topics for conversations ... our equivalent of talking about the weather, I s'pose.
Now there's more to our friendship, but without gaming, I'd see him very rarely, having dropped out of contact.
One a non-evangelistic note, there have been a few games that I've played that have led to conversations with God about life, love, ethics, death, evangelism, and other things. Ultima 6 & 7 come to mind, and Planescape: Torment (older games, I know). While these games aren't Christian, they addressed issues that made me want to know what God thought about them. Knowing God more is an aspect of serving Christ.
Disclaimer: While the Flanders quote doesn't apply 100% here, I do have a tendency to rationalize things, so I can't claim it doesn't apply at all.