The problem here is, although all those players might be call defensive midfielders, the way in which they play/played the game was so polaric, you could form complementary pairings from a number of combinations listed.
Gattusso was a very basic runner and presser of the opposition. His job could not have been simpler: run, harrass, get the ball, immediately give it to far superior ball users, but most importantly, get it to another player on his team to do something with. Gattuso had zero expectation placed upon him to do anything creative or proactive with the ball.
Kante is a halfway house between Gattuso and the players in italics, as they are all able to move with the ball, make space to receive it back and be progressive.
The bolded, however, are instrumental in progressive passes between the lines to another team mate and are key components in massive retention states during a game. You can go as far as to state: you shut those players down and their sides lose a lot of what makes them so dangerous. Javi Martinez came up as a really impressive user of the ball and little by little, he relinquished this at Bayern, but certainly in Spain, he was a player we could do with a carbon copy of right now.
We definitely shouldn't be looking at a Gattuso type, and if we're lucky, we manage to get a player from the bolded archetype as they control games with effortlessly subtle and consistently damaging passes.