it actually takes at least one month.
ONE recent example is this case :
https://boards.na.leagueoflegends.com/en/c/player-behavior-moderation/jFwTE8Oj-playing-off-meta-in-ranked-int-feeding-ban
The guy received over 500 reports over a month and a little, and only then he was flagged for manual review.
The guy hard griefed and trolled every single of his games, down from lvl 1 up to lvl 43. Every single game he tried to lose. Yet he only got checked after 42 levels, after 5 weeks, after 500 reports and after who knows how many handreds of games.
Another example is the OP's screenshot. I remember that case, it is too old. (not sure if its the same case or a similar one). But that guy was trolling for OVER one month too. He had lost around 100 ranked games in a row with nunu, propably received around 500 reports also. He only got banned after all of that...
(edit, its a different one. the OP's case is recent and from korea. the case i described was from 2016 i think, in west.)
edit : another case : http://na.op.gg/summoner/userName=%C5%BEyzz . banned after 72 troll games in a row OF RUNNING IT DOWN 3-5 times and then going afk farming jungle. trust me, if he didnt run it down 3-5 times at the start of each game, he would have been banned not after 70 games, but after 170. because the only "trolling" behavior riot DOES insta ban even if done only in a couple of games, is intentionally feeding. and still, they dont ban all intentionally feeder, rather than only the few stupid ones you run it down to opponent turrets and are stupid enough to admit it in the chat.
One thing is certain. Behaviors of trolling, griefing, and generally trying to intentionally lose a game, are only punished if they reach the above scale/magnitude. People who only troll/grief occasionally from time to time, just DONT get punished. period.
When riot comes forward and says such behaviors warrant account suspensions even after a single game, is just theory. noone ever gets banned for trolling/griefing unless they do it in every single game they play, for over a hundreds of games, for over a month.
