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Yes, biblical canon is a necessary and important alternative and/or companion to this tag. However, there can exist games designed to promote Christianity and biblical themes but not actually based on the Bible. For instance, if there were a game made about John Newton's life. And, any game creator can base a game on the Bible, and even do a really good job, without being a Christian themselves. Also the resulting game may be of the utmost quality and adherence to the Bible (biblical canon), without necessarily promoting the material, and could in fact belittle it through selective context. Finally, Judaism, Islam, and Christianity share some of the same scriptures and yet are opposed to each other in some key ways; biblical canon is not equivalent to Christian anymore than it is equivalent to Islam or Judaism. And 'christian author' is more of a subset of this tag, not a synonym. There are thousands of Christain game authors that are working on normal everyday 'secular' games without adding anything 'Christian' to them; as is the case with Buddhists, Jews, and Muslims. It would be rather silly to tag Doom as a Mormon game because Sandy Petersen is Mormon.
There is a whole list of similar tags, btw. You seemed to have single out 'christian'
Buddhist Faith
Catholic Faith
Christian faith
Jewish Faith
Mormon Faith
Muslim Faith