The question here is, do you think subgenres like gothic, nu, and alt still count as metal?
I think gothic and nu do, but alt is kind of on the line between metal and hard rock. Hence (in my mind) why it's called 'alternative'.
As a second year music student, I've been taught to think of Metal as an umbrella term. Nu Metal, Gothic Metal and Alternative Metal are all subgenres of the collective 'Metal' genre, along with many others such as Heavy Metal, Thrash Metal, Death Metal, Industrial Metal, Black Metal, Speed Metal, Power Metal, Symphonic Metal, Metalcore etc.
Alternatively, what you would class as 'real' metal is purely up to the listener. Technically speaking, 'real' metal, i.e. metal in its purest form would be Heavy Metal because it was the first to emerge, played by bands such as Black Sabbath, Ozzy Osbourne and Judas Priest. Hope this helped!