I don't think their style is anything new or unique.
They're a relentless forechecking team and they're good at taking away space and time and are unpleasant to play against.
A lot of teams can try to play that way, but their success isn't predicated on playing scrappy, heavy hockey alone. They have a lot of talent and depth (and yes, they do have a few rat type players, making them all the tougher to play against). Hell, CAR plays a similar style but isn't as gritty or rough and doesn't have close to the high end talent or depth FLA has.
When Tampa was winning their Cups, they had unbelievable depth. PIT won one year with Crosby winning the Conn Smythe with 19 points.
Regardless of style, teams with elite talent and good depth are the ones that tend to come out on top.