So how would I categorize his directorial style? That's a complicated question, but I'm going to try and answer that in the paragraph below.
Guy Ritchie puts hard-hitting fast-moving action sequences into his shows. They are typically violent and bloody, hand-to-hand combat...and where guns are concerned you want to think of the phrase, "gun kata," which is best pictured as a kind of martial art only with guns involved. He also uses Quick Jump cut sequences, which Ritchie leans on to show a character performing an action that isn't important to the plot, but is useful for building context for understanding the character. Ritchie also ignores a traditional exposition in storytelling by beginning mid-stride, and it's up to the audience to catch up. He also uses vibrant and memorable characters. Sometimes they are over the top, like Brad Pitt's Mickey O'Neil, who is a hot-headed Irish boxer who is purposefully difficult to understand. Last (but not least) Ritchie tints his films. The Sherlock Holmes movies have a blue color purposefully overlaid on the film stock (it was used in another movie called Man of Steel) and it washes out color and makes things appear cold and hard/unforgiving.
So all of these things work in some instances, but they don't work for me in others. Do I think Guy Ritchie is the right director for a musical like Aladdin? No I do not, and I think it's going to be really weird. Will Smith as the Genie might work (His comedic timing in Men in Black is pretty good). And the fact that I've always loved the ancient story of Aladdin means that I'll still go see it (especially just to see the Cave of Wonders), but my expectations are already low. Why did Disney go with Guy Ritchie? Do they not understand their own intellectual property? If Aladdin features any of Guy Ritchie's signature style, I think it will woefully miss the mark both in the terms of diversity as well as storytelling.