Gary Gygax . . . explained that he felt it unseemly to include anything too explicitly Christian in a mere game, even if he assumed a kind of quasi-Christian or crypto-Christian underpinning for the whole thing.
In my experience, Gygax is fairly representative of the gaming community — that to explicitly include God in the equation is uncomfortable, odd, or downright blasphemous. I find it ironic (and not a little telling) that this discomfort has contributed to a trajectory that has led to polytheism being explicitly expressed in the game system. That gamers have no problem with various iterations of pagan gods, but hesitate to include the Christian God because D&D is a game, suggests that gamers implicitly understand pagan gods are fictitious whereas the Christian God is very real.
As an Orthodox Christian, this phenomenon reminds me very much of a guy named Nestorius. The word "dogma" in modern America has a lot of baggage, and is seen by many to be a bad word. However, Orthodoxy has long understood that belief systems have consequences — they result in behavior. This behavior, in turn, reveals what we really believe.
During the 5th century, Nestor was a priest whose teachings attempted
to rationally explain and understand the incarnation of the divine Logos, the Second Person of the Holy Trinity as the man Jesus Christ. Nestorianism teaches that the human and divine essences of Christ are separate and that there are two persons, the man Jesus Christ and the divine Logos, which dwelt in the man. Thus, Nestorians reject such terminology as "God suffered" or "God was crucified", because they believe that the man Jesus Christ suffered. Likewise, they reject the term Theotokos (Giver of birth to God) for the Virgin Mary, using instead the term Christotokos (giver of birth to Christ) or Anthropotokos (giver of birth to a man). — http://orthodoxwiki.org/Nestorianism
This is in contrast to the Orthodox understanding that Christ is perfect God and perfect man; that the divinity and humanity in Christ are two natures in one person; and that these two natures do not change, are not confused with one another, cannot be divided into isolated categories, nor be separated in terms of area or function.
These different understandings of Christ result in different kinds of behavior. Nestorianism results in the compartmentalization of life — one's work life is cut off from one's home life which is cut off from one's recreational life which is cut of from one's religious life. This results in a kind of schizophrenia, where one becomes a different person for every aspect of their life. I actually know of a guy who politically claims to be a communist, who religiously claims to be Christian, and economically is a ruthless, exploitive capitalist. This schizophrenia allows us to justify destructive behaviors, because we believe that the behavior of one aspect of our lives does not affect the others. This, of course, is an illusion.
In contrast, the Orthodox understanding of Christ leads us towards a holistic understanding of the human person, where everything we do affects every aspect of our lives. Thus, Gygax's notion that including Christianity in a mere game is unseemly makes little sense to my Orthodox mind. My belief in Christ must necessarily inform my role playing. One of the reasons I feel more comfortable with older versions of D&D is that the game system, by implicitly assuming Christianity, makes this possible. As we have increasingly put D&D into a box, trying to isolate it from this aspect of its heritage by systemically requiring polytheism, the more schizophrenic it has become.
We have been given the illusion of freedom — more choices for creating characters, creating monsters, creating magic items, etc. However, since all of these creative processes have been systematized, we are far from free of doing things in our own unique way. If we don't follow certain paths, we've thrown the game out of balance and/or broken the game. I cannot speak for 4e, as I have not actually read or played the game. However, judging from the reactions of many people about the game, its affinity to video games and for reducing every aspect of the game to a formula does not bode well for a systemic support of freedom and creativity.
From my own Orthodox perspective, this does not surprise me. God is ultimately free. He has made us in His image and likeness, thus giving us freedom. When we freely choose to bring Christ into every aspect of our lives, we experience His freedom. When we freely choose to deny him from any aspect of our lives, we step into the illusory world of sin and darkness. We imagine that we are free, but we are limited by our passions, our sins, and our fallen nature.
This is the very reason I freely choose to embrace the Christian roots of the game of D&D, and carry it through into my own gaming experience.