Since I can't play DMC games right now, I tried to find a Flash version, or at least a substitute. And so I came across Fear Unlimited. Of course, being a flash game, it is rather simplistic compared to DMC PC games. Ranks appear to be based on raw damage output, there is a limited number of moves, but it does try to get at least some feel of the DMC. Moves that do appear are taken from DMC.
https://www.newgrounds.com/portal/view/279998
https://www.newgrounds.com/portal/view/279998