Intro
Let it be known that the following is heavily opinionated, but based on teachings. I personally struggle with taking stories in any medium that use angels and demons. I am a little more forgiving about depictions of demons but I'm still picky. I have yet to see or read something that really satisfies outside of Scripture or the lives of Saints or C.S. Lewis' Screwtape Letters.
Depictions of Angels - Tales of Symphonia, Bayonetta
Starting with Angels, I thought of two games both originating in Japan: Tales of Symphonia and Bayonetta. In both games, Angels are considered villains to fight. (It's more subtle in Symphonia). In Bayonetta they appear more abstractly while in Tales they are more human.
The theme is usually that angels are a race of arrogant beings that are hung up on virtue and exist solely to stop demons or prevent humans from becoming evil.
Depictions of Demons - Disgaea, Dragon Age, Dante's Inferno
Demons seem to have a wider range of interpretation. In Dante's Inferno and Dragon Age, demons were creatures/monsters that personified a deadly sin. They are always evil and always monsters. This seems to be a common theme in games with a few exceptions.
In Disgaea, you play as a demon trying to reclaim your throne as overlord of the Netherworld. Demons are depicted as petty and power hungry, but redemptive. Meaning they can repent and be "good".
East vs. West
The idea of Puritan, Tyrant Angels and good-hearted demons is more often found in games from Japan. This comes from a different cultural perspective in which spirits are neither good or evil. (Like fairies.)Yokai is usually translated as "demon" in English but does not mean the same thing as the Christian idea of 'demon'. Yokai are folklore monsters and shape-shifters that can be good or evil. In most Japanese games where you fight "demons" it is more likely you are actually fighting Yokai. The same could be said about Japanese Angels.
In Western culture, it is also common to depict demons as monsters, but stories and games never depict them as something that could possibly be good. Demons are always evil and never trusted. Dragon Age had a good visual representation on Western belief of demons and their relationship with humans. 1) They really could never be trusted they only want power for themselves. Possessing a human to move in the physical world was the goal. 2) Humans/Elves infected by a demon became deformed and ugly. (The effect of sin on the soul. ;))
Angels tend not to show up in Western games too much. Sure there are the "good spirits" in Dragon age as well, but I've talked enough about that game for now. Moving on.
Catholic Teachings
There is this theme in the use of supernatural and that is its involvement in the natural world. This is probably the only point in which the depictions of angels and demons is true. For a Catholic, Angels and Demons are not creatures of myth or fantasy. These are real supernatural creations. As humans, it is impossible for us to understand their true nature as they are beings of pure spirit and perfect reason. However, we find lots of influence from history, art and Tradition in our understanding.
As far as Angels are concerned, meeting one was usually a TERRIFYING event. In Scripture, those who met with angels had to be comforted with the words "Be Not Afraid". This suggests that the sight of an angel is a lot for a human to bear. People usually fall on their faces.
The role of an angel is to serve God at his throne, but also to act as messenger. The word angel comes from the Greek word for message.
Demons are the other side of the coin. Demons are fallen angels in Catholic tradition. And meeting with a demon is as terrifying as meeting with an Angel. However, they are conquered by the Salvation of Christ. A demon can be exorcised or banished from this earth.
More about angels and demons can be read about here:
(TBA)
Conclusion
I am a fan of anime and Japanese games, but I am uncomfortable with teaching the concept that demons are just like people with bad habits. A healthy dose of caution is necessary to protect one's soul. Most of my problems with "incorrect" depictions is from my belief that these are not fantasy creatures made up by our ancestors to scare me into being good. The rules of fiction are looser for creatures of fantasy like unicorns and fairies. However, a creature that exists in reality does have a correct depiction and a wrong one.
Reducing the supernatural to myth is dangerous. Myth can help us by being a lens to understand reality.
However, that doesn't mean that angels and demons can not be in stories or video games. Just take the time to do the research.