The system is fully automated (manual reviews to happen for fringe cases and randomly, but mostly it's automated). When anyone in a match reports a person, that game is now flagged. When that player receives too many reports across too few games, their case will be reviewed and the system will check all the flagged matches; if it finds the player to be consistently or extremely toxic, it will hand out punishment appropriate to the offense and to where they are at on the 4 tiers of punishment.
It's possible that this player never receives any more reports and does not have their case reviewed, and this lenience is a good thing for most people that just have a one-off bad day, but if he continues behavior like this he'll get punished accordingly.