Guardiola & co. changed what box-to-box used to be quite a bit, as back then it was normal instead of slowing the game down to rush forward with the ball after gaining possession like Matthäus often did. Having all-around qualities contributed to that style if anything.I'd call him all around midfielder (not box-to-box midfieder), as he did all types of things on the pitch.
As I said, it depends on the definition of defensive midfielder. I'll reserve that definition to players like Busquets, Redondo or Makelele.