As far as the AI is concerned, it's mainly used for roster management as it pertains to the promotion's product. It's also supposed to be a hint at where a worker's strengths lie, skillwise. When you see a psychopath, you expect high hardcore, brawling, and toughness. Likewise, a cruiserweight will tend to have aerial and/or flashiness as a key skill. On a meta level, it also gives you an idea of what a worker will switch to when their skills progress/change. If you're running 5SSW, for example, you'll notice many workers will switch to Japanese Junior (Key Modern) or Brawler or Puroresu (Key Realism) but almost never to Entertainer (no Mainstream in the product). Whereas if you were running AAA, it would be the opposite (workers falling over themselves to switch to Entertainer).
The only real ingame effect I've seen is for AI roster management. For example, I've noticed that EMLL let Pyromaniac go in pretty much every game I play. He's not a terrible worker (especially for the bottom of the card, where he typically resides) but his style (Psychopath) doesn't fit their product so whenever his contract comes due, they don't even offer him an extension. Mercy Michaels is similar in that his style (again, Psychopath) prevents him from being signed to promotions who could use him at the bottom of the card. He's got nice performance skills (basically, a less expensive Ben Williams) but it would probably take a human user to sign him and let him switch styles (almost certainly to Brawler) to make the AI see that.