Dante from the first Devil May Cry was inspired by Blade the Daywalker, the Marvel comicbook character played by Wesley Snipes in the movies. Like Blade, Dante is half human and half something supernatural, in this case a demon instead of a vampire. They both fight with swords and guns, they both wear trenchcoats and have a stylish fighting style.
Demons trying to come through to the mortal world and make it their own has been seen in many many movies, also great Hollywood blockbusters. So it isn't just Ninja Theory/Tameem who gets inspiration from Hollywood movies, Dante and Devil May Cry have always had that movie flair to it. I'm actually baffled that there hasn't been a movie about Devil May Cry yet.