The court applied the Turner test, which is very similar to the rational basis test: the plaintiff was burdened with showing that the threat of gang formation was "so remote as to render the policy arbitrary or irrational."
This may strike some as odd, given that 1st Amendment cases typically use strict scrutiny, not rational basis. But, here's the catch: it doesn't apply in prison! In prison, your 1st amendment rights are more limited, and something akin to the rational basis test does indeed apply. To quote the court:
"In Turner, the Supreme Court determined that prison regulations that restrict inmates' constitutional rights are nevertheless valid if they are reasonably related to legitimate penological interests."
So, despite the apparent silliness of banning D&D, it seems the prison was within its rights to do so. The prison system may, at its discretion, inflict all kinds of petty punishments upon prisoners. If you're sent to prison, your rights are sharply curtailed. That's what the court decided in Turner, so that's the way it is.
Whether or not this is good policy is, of course, open to debate. It depends on what balance you want to strike between the punitive/rehabilitative purposes of prison. I'm of the opinion that criminal justice ought to be primarily aimed at reducing recidivism, but then society at large doesn't really agree with me.
Here's the full decision:
http://caselaw.findlaw.com/us-7th-circuit/1498113.html