Fridge Brilliance: DmC: Devil May Cry was confirmed to take place in an alternate universe (eventually) from that of the games in the original continuity. Interestingly enough, Devil May Cry Volume 2 (which takes place prior to the events of Devil May Cry 2 in the original continuity) features interdimensional travel between parallel universes as an important Plot Device. Bonus Points for the fact that the primary alternate universe that Dante is in for most of the Novel is one where Mundus DOES rule the human world. Strange fate. Isn't it?
Fridge Brilliance: The style system in this game is mostly based on damage, but it makes sense; this Dante is a fighter, a survivor, he's punk-ish and unrefined. This Dante is angry at the demons who have caused him pain. It would make sense that brutally dismantling his enemies, and causing as much disorder on them as possible, in his view, is being stylish, because he's still in the process of maturing. Considering that he gains several of the old Dante's traits later on in the game, especially at the end where his hair permanently goes white, he starts to refine his fighting style, allowing more creative options, just like the old Dante.
Can also lead to another case of Fridge Brilliance: the game is also easier because Dante has been fighting demons since he was a child, by necessity. So he's already experienced in dealing with the common mooks by the start of the game, hence the easier difficulty.
Another case of Fridge Brilliance is the full realization of the latent ideas introduced in the first Devil May Cry that were never elaborated on. Mundus's name is derived from "Rex Mundi", which was a name that the Cathars used to refer to Satan based on their Gnostic-like beliefs that he was the true ruler of the physical world. Though in the case of DmC: Devil May Cry, the creators choose to portray the resistance to Mundus (as the Demiurge) and his associates (as the Archons) in political/socioeconomic terms (in this case making Mundus the representation of the Dominant Group Culture) rather than in a religious/philosophical way. Whether it is done successfully or not, your mileage may vary.
Mundus is one of many Satanic Archetypes in fictional media who were originally supposed to beSatan himself (name and all), and one overarching theme in The Illuminati conspiracy theories is the premise that Satan is the entire outfit's overarching leader, so yeah, it does make sense.