The Devil May cry games are thematically under the fantasy/dark fantasy type of video games. The themes do differ from each other over the games:
DMC 1 and 3: Classic dark fantasy theme (i.e. creepy gothic towers and castles), all in a contemporary setting
DMC 4: Medieval-ish/Renaissance-ish (based on Fortuna's architecture and design) contemporary dark fantasy (due to the interior fo Fortuna's castle, the hidden pit, etc.)
DMC 2: 90% urban fantasy, 50% science fantasy, 10% dark
DMC 5: Pure urban fantasy with a dash of science fantasy, almost like the Mortal Instruments, Buffy The Vampire Slayer, etc. This is contemporary/urban fantasy done right.
DmC: Devil May Cry: Tries WAAAAAAAAAAY too hard on the teen urban/science fantasy theming motif; littered with corporate images about obesity, soft drinks, etc. Steals too much from Buffy, Twilight, Futurama, Mortal Instruments, etc. Itsuno and the DMC 5 team both did it better than Tameem and NT!