No I wouldn't say it's not a Devil May Cry game. I wouldn't say it at all. At least for me, it felt like Devil May Cry. And I found it fun and solid as a game on its own too.
Combat wise, yeah there are some things that made me cringe that made it feel kind of a step back, primarily the decreased variety in moves and possible combos, especially compared to DMC4, and the overall difficulty.
But that didn't prevent me to enjoy the game or consider it Devil May Cry at its core.
Too bad you didn't feel the same, buddy, but I get it each of us is different.