As a devout Baptist minister, this is likely about one of two things, avoiding the appearance of evil (gambling, 1 Thess 5:22 - Abstain from every form of evil), and giving up something for the sake of others (gambling addictions within the church, Rom 4:21 - or do anything that causes your brother to stumble).

The reality is that most churches recognize that they were too legalistic in the past, and so now address things like gambling more directly, and are perfectly ok with playing cards. FWIW YMMV :-)

I knew plenty of Midwestern Baptists that didn't participate in the triple crown of no-nos: dancing, drinking, and gambling. And cards aren't necessarily gambling, but cards are the bricks that pave the road to such evil. It's guilt-by-association (and some will tell you, wrongly, that playing cards are an outgrowth of tarot cards and the like), but there ya go. Oddly, I knew plenty of Baptists that played Yahtzee, which involves dice, and that seemed acceptable. Never minding that the Roman soldiers cast lots ("dice") for Jesus' clothing. :-)

Consider some writing contemporary to Rockefeller (there is a section on cards): https://baptisthistoryhomepage.com/social.amusements.willis....

Consider that Titan was written maybe 100 years removed from the events and you're reading a secondhand telling of it from a blog. Maybe there is more context in the book if you're really curious, or maybe the context was lost from Rockefeller's time to the book, or from the book to the blogpost.

Consider a few more things: If you ask 10 Baptists about something secondary to scripture like this, you may get different answers from different people, especially if they are from different eras, as religion changes over time. As another example, some Catholics grew up hearing the mass in Latin.

It's funny though, Rockefeller appeared devout enough to understand that gambling was a sin. Rockefeller appeared to believe in an omniscient God. Did he really think his square counters would fool said omniscient God? People trying to find such loopholes in Religion is always fascinating to me. Of course, it could have all been a show.