I read a Japanese food manga (graphic novel series) called Oishinbo. The plot is that there's a food rivalry between a journalist and his food overbearing scholar father involving two rival newspapers competing in a series of cooking battles that spans years. (This ties into the episode. Bear with me.)
The battles would be who can cook the better salmon dish, the better rice dish, etc. The outcome would usually hinge on some minute detail about the consideration and care put into the dish. For example, one battle involved the father character saying that his old non-foodie friend once cooked a simple clams with rice dish that is better than anything his foodie son would be able to cook, which turned into a challenge. The son spared no expense to get the best clams and rice and such and made a great dish, but then the father's humble friend made a dish that was better from cheaper ingredients. The secret being that the friend painstakingly sorted through each clam and grain of rice to remove any that were imperfect to radically improve the end result.
The documentary Jiro Dreams of Sushi about the first sushi place to get a Michelin star shows the same mindset in a nonfiction setting. It's not that the chef is inventing new cuisines and techniques or that he's lavishly throwing delicacies at his patrons (this is a hole in the wall literally in a subway station), he's showing ultimate care and consideration matching food to his patrons. At one point he explains that he cuts a slice of fish a few millimeters thicker for the person with the bigger appetite, and the notices when a patron is left handed and places the dish to that person's left hand side. It's observation, knowledge, judgement, effort, and skill more than inspiration and innovation.
I think the challenge actually did an excellent job in presenting this foreign mindset and that the chefs were game to the challenge. Every course conceptually fit within the parameters well enough, to my knowledge. I compare that again to the ill-fated All Stars dim sum challenge in which I would straightaway eliminate 1/3 of the dishes conceptually as inappropriate.
I think the actual cooking facilities turned out to be a bigger obstacle than the Kaiseki parameters. Having to McGyver a grill sunk Karen (who couldn't choose not to grill), and having to rely on an unfamiliar steamer adversely affected Melissa. I think that's my only complaint about the challenge setup, that they weren't provided the specific equipment to do their required techniques.