At the 2014 Asian Games, Ri qualified in first place ahead of the 2012 Olympic champion on vault, Yang Hak Seon of South Korea, but finished just missing the bronze medal by the narrowest of margins (0.001) with an average combined score of 14.799 on the individual vault event behind Shek Wai Hung of Hong Kong (15.216), Yang Hak Seon (15.200) and Hung Xi of China (14.800).

At the 2014 World Artistic Gymnastics Championships held in Nanning, China, Ri defeated the reigning World and Olympic Champion Yang Hak Seon after Yang crashed in both his vaults during the event final, and won the gold medal with an average combined score of 15.413 ahead of Ihor Radivilov of Ukraine (15.333), 2012 Olympic bronze medalist on vault, and Jacob Dalton from the United States (15.199).

On November 1, 2015, Ri participated in the 2015 World Artistic Gymnastics Championships in Glasgow, Scotland, and successfully defended his individual vault title.

He won with an average combined scored of 15.450 ahead of veteran Marian Drăgulescu of Romania (15.400) and Donnell Whittenburg of the United States (15.350).

At the 2018 World Artistic Gymnastics Championships, Ri won gold with two of the highest 6.0 difficulty vaults and an average combined score of 14.933 ahead of Artur Dalaloyan of Russia (14.883) and Kenzō Shirai of Japan (14.675).