So, with this post on reddit, and this Facebook group, I was able to find many of Korea's top player's masteries. First, after going through pages and pages of masteries (used in OGN, not solo queue), I'm going to write the general trends that I discovered:

1. I couldn't find a single example of a Mid laner or AP running anything other than 21 points in offense. Where the points went differed obviously, but the overall choice seemed to be going down the left or right side of the offense mastery tree.

2. No AD carries get any points in Havoc, while every midlaner did. It seems the 2% increase in damage was appreciated more in the burst damage aspect of mid laners. However, AD carries preferred to put those 3 points in Lethality and Frenzy, for the extra Critical damage and buff. Even Score's Ezreal, which doesn't get any substantial crit chance till his third item, (Triforce into LW into IE) chose to spec into those two points rather than Havoc and the extra 2% damage. The Triforce crit chance is low enough that taking the points into Havoc would be more cost effective before getting your IE and more crit chance, so this seemed kind of odd.

3. ADCs, Top Laners, and Mid Laners taking 2 points in Butcher for last hitting. Now unlike the other two, this one had exceptions, with Faker never running butcher, but Ryu took it whenever he wasn't playing Zed, even taking it on Karthus, who rarely uses autoattacks to last hit. For Rapidstar it appeared to be situational, as I found one Ahri game where he ran it, and another where he didn't. Also, top laners ran it less often than their other teammates, but there were a few examples. Every AD ran it every game I saw.

4. Korean Junglers all love running 21/9/0 on offensive junglers, specifically Elise, Evelynn, Vi, Lee Sin, and Jarvan IV. What I found particularly interesting was Kakao's Elise and Evelynn page:

Now, since Elise and Evelynn are both AP Junglers, going deep into the left side of the offense tree made sense, but leaving Spellsword (ap deals on hit damage) and Archmage (+5% of your AP) and favoring straight AD and Armor Penetration was confusing. Clearly the AD helps with your jungle clear, but doing the math, it seems that Archangel and Spellsword offer more damage in the late game on AP junglers, so it seems that Kakao is really going for the early game pressure with these masteries. In addition, with the huge popularity of Armor Yellows, Armor Penetration couldn't hurt.

5. I couldn't find a single example of anyone taking Legendary Armor (+5% bonus armor and magic resistance), or Defender (+1 armor and magic resistance for every nearby enemy champion). However, every mastery page that put 21 points into the Defense Tree opted for Tenacious and Juggernaut. It seems that the Defense Tree is pretty set in stone of what you should run, with only slight deviations.

6. Last and probably most interesting, was the support's pages. 1/13/16 was THE page for Korean Supports, on every Support Champion. Madlife, Mata, Muse, Poohmandu, all ran 1/13/16, the following page.

They would all run this, or some slight variant. And this was the majority of players, including the one and only Madlife. However, there was another school of thought, which seems to be led by KT bullet's Mafa, and Lustboy, and a select few other team's supports all seemed to prefer running 9/0/21 or 0/9/21, and really spec into the utility tree as deeply as possible. However, the majority ran 1/13/16.

Well I hope this helped everyone and that you were able to learn something! I'll be doing something similar for Korean runes in the near future after Team Dignitas' World Championships coverage is over! Good luck on the Fields of Justice Summoners!