The game repeats after that. There's additional features on each loop that add to difficulty. It's not possible, for instance, to king only round 2 as there's mines on the ground and they guard the castle entrance. Your king's max power is also reduced as well.
It does not loop after each round/level. As stated above: There's a significant alteration of the difficulty and new challenges. It is not possible to 'king only' past the first level, and unless you manipulate an extensive amount, you'll need to use a lot of strategy!
It does use mostly the same sprites and layout though. It's a pretty old earlier 80s game that was ported to Famicom.
It also adds a mark after each level you win. The marks stop after 6. I forget if you get 'level 1 again' or 'level 6 forever' after completing the last new board or if the game actually ends.
It's been some time and I'd like to get back to it but I've not had the time.