There's still one more event to go, but here is some initial stats on the performance of nations in non-Olympic events.
First I removed all non-Olympic sports, except for roller sports, which I only kept skateboarding. I also removed events from Olympic sports that are not in the Olympics with the following exceptions. In boxing, weightlifting and wrestling all weightclasses were kept and in karate the men's and women’s +84kg and +68kg respectively were kept to simulate the +75kg and +61kg events.
Medals won in non-Olympic Events
1. - 63
2. - 59
3. - 52
4. - 34
5. - 32
6. - 25
7. - 24
8. - 23
8. - 23
8. - 23
11. - 22
Everyone else won fewer than 20 medals in non-Olympic events. Not too surprising that Indonesia won the most medals. Bahrain, Iraq and Syria were the only nations to have won medals, but none in non-Olympic events. Afghanistan, Cambodia, Laos, Myanmar and Nepal only won medals in non-Olympic events. Of course putting down total medals is a bit unfair for larger nations. Powerhouses like China are expected to do well in all sports so it's expected that they would also win more medals in non-Olympic sports.
Here I calculated the probability that a nation would have earned their number of Olympic event medals (or fewer) over the total medals won. A lower number meant it was unlikely and that the nation likely benefited from non-Olympic events.
1. 0.0000000076%
2. 0.0049%
3. 0.0087%
4. 0.049%
5. 0.12%
6. 0.35%
7. 0.84%
8. 2.46%
9. 3.34%
10. 4.39%
Everyone else was at a 10% chance or higher. 8/10 nations that benefited from non-Olympic events were Southeast Asian nations, likely due to Indonesia's influence. The nations that saw significantly little to no benefit from the added events were Bahrain, Iraq, Syria, Japan, China, North Korea, Qatar and Kazakhstan.