The Cardinals Way is their organizational philosophy of "We're the best, because we say we're the best" which also floods into their fandom, and the media with just how classy their organization is.
It's also a crappy book written akin to Moneyball, but geared specifically to pilfer the wallets of Cardinals fans who are also Rubes.
The Cardinals Way has been around since LaRussa was passing out drunk while driving, encouraging steroid use and ordering pitchers to bean opposing hitters if they dared throw inside to Pujols.
It's been around since they hacked the Houston Astros player database.
We mock it here for the pompous arrogance that their fans and organization continue to show and continue to be propped up to by the media.