Here's perhaps a clearer example of what defines a hack and slash, between games technically in the same franchise.
Take the Legend of Zelda and its spin off, Hyrule Warriors. Mainline Legend of Zelda games do not focus around hack and slash combat. There's no emphasis on combos, minimal variety in melee attacks, switching weapons isn't seamless, and Link generally doesn't move very fast. None of these are inherently bad things; and Zelda's combat fits a game tending more towards exploration like it is.
With that said, take Hyrule Warriors. There's a heavy emphasis on combos, a number of different attack strings you can pull off (though it's a lot less than something like DMC or Bayonetta), and characters move extremely quickly. There's a sense of flashiness to the combat that mainline Zelda titles don't focus on.
That's what really makes a hack and slash game, a hack and slash game. So far, from what we've seen (and admittedly, this could very well change if the E3 demo is unrepresentative of the finished product), God of War 4 doesn't fall into the latter category. Kratos seems pretty slow with the exception of his dodge move, and combat is far less about variety and combos and more about simply running up and mashing the attack button.
