Thanks for the suggestions, the both of you. They have the basis for some good game play.
I think, though, that perhaps I am not being entirely clear. I'm curious as to what aspects (or aims, or goals) a game should have to make it interesting, engaging, and desirable to a Catholic, for themselves and their family. As an example, I put forth my own desires in Catholic games for myself and my (future) family.:
Children: Basic understanding of Bible stories and religious facts (Adam and Eve were the first people created by God, and God is Jesus's Dad, for example)
Preteen: Intermediate understanding of Bible stories and religious facts, basic understanding of catechism, basic application of moral law (Holy Trinity as one God in Three parts, simple subtext in parables, age-appropriate applications of catechism and moral laws to self)
Teenager: Advanced understanding of Bible stories and religious facts, intermediate understanding of catechism, intermediate applications of moral law (Understanding of symbolism and subtext in passages, recognizing pope's right to rule, ability to understand applications of catechism and moral law to others)
Adult: Focused on honing areas of interest, such as Apologetics.
So, a game for Children could well be a Candyland-style romp through Bible stories, the trivia game could have difficulty sets for all ages, a Teenage-focused game might involve invoking sound judgment in the form of matching teachings to problems to succeed, and an Adult game could focus on resolving moral ambiguity.