Great question, though I’m not completely sure about what would count to you as “beneficial”.
To me a well made Christian game would benefit people by drawing them closer to God. So one way to approach it might be to think about what has done that for you personally, and whether that can be translated into something interactive.
One of the influences on my becoming a Christian was, strangely enough, a series of fantasy books (The Dragon King Saga). Being a lover of fantasy stories, this somehow reached past my defenses as I followed the main character and his developing relationship with God. I also enjoyed The Archives of Anthropos a few years later.
Both of these series had allegorical aspects, which helped to avoid feeling preachy, because the message was indirect. But they also presented God as a relatable person that (some of) the characters got to know better over time. The most impacting moments were when a character revised their picture of God, finding that he was more amazing, merciful, overwhelmingly kind or whatever else they hadn’t seen in him before.
Unfortunately a moment of revelation and personal crisis can easily lack authenticity (as in the Christian movies mentioned upthread). This might also be hard to translate into something interactive, since it is so subjective. But it could work if there is enough groundwork beforehand and it is the logical place for the story to go (e.g. a build up of events for which an inner crisis is the natural conclusion).
A life changing crisis isn’t obligatory to be a Christian story, though. People grow closer to God through less dramatic means, such as seeing his consistent character, small experiences of his love that accumulate together, experiencing his presence, learning to hear his “still small voice” and other things.
It can be helpful to think about the specific message you want to get across (even if it will be indirect). If I wrote a Christian story, I think I would want to undermine common misconceptions about God (e.g. God is not an impersonal force but someone you can know as a real person). Have a think about what “burns in your heart” about God, and what you are really passionate about – what kinds of plot events might carry that message? Beware of unintentional messages too, e.g. a story focusing on growth and change could be taken as, “Christianity is self improvement”.
One more thought: God can be surprising; what do you expect from someone with infinite wisdom? This could be difficult to model if God is a dynamic character in the story. I like the idea of a game where you can interact with God in some way, but not if he is too predictable.