The Ikemen team consists of the guys named in the tags, Maki Horikita (Mizuki's actress), and Ryo Kimura (sorry, I'm not sure/don't remember which character he plays because I'm so terribly behind on HanaKimi).
Anyway, there seem to be three games. First one is where the contestants stand behind a (sort of?) podium (similar to one on a standard quiz show, I'm thinking of Jeopardy!) From left to right (as viewers see them on screen): Maki, Mizushima, Yamamoto, Rashi, and Kimura. They are supposed to answer a question, but each person is responsible only for his/her part. For example, there is one question that says "fifty-four thousand and three hundred" in English. So the first person on the left would have to answer "5", the next one "4" and so on, so when the viewers look, the whole answer says "54300".
The next round is riding in the big carriage(?) through all the scenery from different countries. This part was so fun, but then I so love this kind of simulator rides at amusement parks. There is one designated person to answer the question (typing in the correct Hiraganas for the Kanjis thrown (literally) at them, if I'm not mistaken). If this person makes a mistake, the next person will get to answer. I'm not sure how many times you have to get it wrong until the game is over, though. Of note, Rashi didn't get even one correct answer in this round, whereas everyone else did. (Although it was Mizushima who finally doomed them with "Game Over".)
The last round takes the contestants back to stand behind a podium, but this time there is a bomb over their head. The bomb starts off on the left most person's head. If he/she can answer the question, the bomb jumps over the head of the next person to the right. If the right most person answer correctly, the game is clear (bomb disappears) and they get points. Otherwise, the bomb explodes over the head of the person who can't give the correct answer. I think Rashi got the bomb exploded in the second level of this round. (Although it was Maki who finally doomed them with "Game Over". Ha ha, she didn't even attempt to answer, just kept repeating "I don't know, I don't know" (I think).)
The Neptune beats the Ikemen, so they get to go on the bonus round. This game is similar to the second game, in which they ride in some moving thing, although they all standing in it this time, and the scenery looks more to me like inside of a mine or a volcano. This time, however, all players decide on the correct answer. They have to choose from two answers on the right and left. If they choose the answer on the left, their moving car goes through the left; if they choose the answer on the right, their moving car goes through the right. The danger is if it is the wrong answer, the car would fall down through the lava-looking liquid.
Want to say more about Yamamoto (he seemed particularly funny in one part--reminded me a little of his role in Kabuto; wish I understood what he was saying), but he (and the other guy) didn't seem to have made major mistakes like Rashi and Mizushima did.
(I'm sure the show is scripted to some extent, but I can't really tell which part(s). Besides, it's still fun anyway.)
Oh well, sorry if this doesn't make much sense. For me, I'm going to look at more NEP League and hope that the format would stay fresh for a while. (Meaning I hope I won't get bored with it if I don't see some familiar faces in this show.)
Screencaps (taken from UltramanLah!--thanks for making me aware of this show in the first place--because for some reason I can't cap my own):