In the Gen Con 2013 Preview, some folks referred to the game as GOSU-like or Citadels-like, but Koryŏ is like those games only in the sense that they all contain cards with numbers on them. A better comparison might be to Mick Ado and Alan R. Moon's Get the Goods as players are limited in which cards they can play each round while wanting to have the majorities in the character cards they collect. Why? So they can use that character's special power during the game and so they can score points for the card type at the end of the game. Yay, special powers!
The game lasts eight rounds, with the number of cards you're dealt and the number of cards you can keep respectively decreasing and increasing over the course of the game. In the first round, you have a hand of ten cards and can have at most three cards on the table at the end of the round; in the second round, you have nine cards in hand and can end the round with four cards; and so on. Each round, players simultaneously play as many cards as they want from their hand, but all cards must be the same character (i.e. number); they discard everything else from their hand, and those discards will be shuffled with the remainder of the deck for the next round.
Players then reveal cards in clockwise order from the round's starting player, and for each majority they have among all the character cards in front of them, they might receive a special power. If you have the most bankers (#6), for example, then you take a 1 VP token from the center of the table; having the most spies (#2) lets you steal a 1 VP token from someone else. After you've all revealed cards and used whatever powers are available to you, you discard cards from the table (if needed) to meet that round's card limit.
Unlike in Get the Goods, the Koryŏ deck uses the structure of The Great Dalmuti, with one 1, two 2s, three 3s, and so on up to nine 9s. In addition to the numbered cards, the deck contains ten events: six barbarian cards and four lobbying cards. You play them as you would number cards — that is, if you play one or more barbarian cards, you can't play anything else — and the event cards let you mess with opponents. For each barbarian played, you can destroy one character card in another player's collection; for each lobbying played, you can swap two character cards between players. The drawback, however, is that each event card costs you 1 VP at the end of the game, so you better make those events matter!
The special powers of the other characters affect everything else described above: broadcasters (#8) let you start with one more card in hand each round while senators (#3) let you keep two more cards; guardians (#7) protect you from barbarians while spies (#2) protect you from lobbying; priests (#4) let you discard one event you've played; ship owners (#5) let you play two single cards of different types, and the omniscient (#1) lets you use character powers in the event of a tie, when normally no one would get the bonus.
At the end of eight rounds, you tally points, scoring as many points for a character type as the number of that character — but only if you have more of that character than each other player. The omniscient doesn't help you here! To this sum, you add points for VP tokens and subtract points for events you played, and whoever has the highest score wins.
I think we spent more time learning the rules for Koryŏ at Gen Con than we did playing the game, but that was because the person initially teaching us had played only once months earlier and was translating from the French rules on the fly. As I've written before, such is the nature of playing games at conventions! Thankfully I used my phone to find the English rules online (go BGG!), and we carried on to discover a quick-playing game that combines majority-scoring and special powers in about as tight a manner as possible. You want to expand in every direction to get bonus powers and score majorities — nine points is huge! — and you want to protect what you already have to keep getting powers, but you're limited in what you can play each round with a fresh hand of cards form which to consider.
If you want a shorter, steamier, more dramatic version of the above summary, here's a teaser video from Moonster Games: