He did the most damage because he had thornmail and sunfire cape, and participated in 34 of his team's 49 kills.
Everytime an enemy champion auto attack him from ~28:00 onwards (when he got thornmail)- he did damage to them and was counted as such in the statistics.
Everytime he was standing around an enemy champion from ~16:00 onwards (when he got sunfire)- he did damage to them and was counted as such in the statistics.
The damage over time adds up quickly.
He also participated in 34 of his teams 49 kills...that is almost 70% of all their kills. The best on your team was Xin Zhao- who participated in 30 of your teams 55 kills (~55%) and not coincidentally had the second most damage in the game against champions.
You have to be very careful when comparing damage dealt to champions in a single game and then drawing conclusions from it. Whenever you see a thread complaining about a tank doing the most damage in the game it is almost always a case where they have those two items.