Screenshots of your settings aren't necessary. You can just post a logfile from %appdata%\OBS\logs and it'll have all that information condensed down along with more useful info.
FPS games are high-motion... you ARE going to get a lot of pixellization and artifacting running 720p video at only 2000kbps, ESPECIALLY trying to go at 60fps. First, you need to drop to 30fps. This will allow twice as much bitrate per frame, as it's only sending half as many in the same timeframe, and improve the visual fidelity a lot. 60fps is mostly just stat-wanking anyway, despite what many 'competitive' players will say. There are only a few cases where 60fps is really necessary for a given game, and first person shooters (and League) definitely are not one of them.
But realistically, you need to drop your resolution further (run at 480p video) as well, to get rid of it more effectively. High motion games REQUIRE higher bitrate to look good, which you can't really do until you become a partner and have transcodes available, without causing many of your viewers to buffer like crazy.
You will NEVER get 1:1 perfect video though, even if you throw massive amounts of bitrate at the problem. You need to mitigate your expectations to some level.