Yes, Obito, Kakashi, and Rin did take part in the war. They are 9 years older than Itachi, so they were 13 when it was taking place.
By looking at that image and the way Obito described it, it is quite evident that he was present during battles.
We don't exactly know how things worked back then. During Hashirama's/Madara's days, 7 year olds were going at it against adults. Now, the genin (bar Naruto/Sasuke for obvious reasons) and younger shinobi are not in the war, but then again times have been more peaceful and the war is occuring in an area far away from the villages. For the war during Itachi's time, parts of it were occuring in Konoha, it would not be hard to miss.
Also, Itachi was the Uchiha clan leader's son. It's not far-fetched to expect more out of him than the other kids his age. In the shinobi world, all you need is a kunai to fight someone (look at that panel you posted and notice how many people died with just weapons) and we know how good Itachi is with such tools. He's also the type that does things from a very early age. Normally, you would expect someone to graduate from the Academy in 6 years...not 1 (much less at the age of 8) like Itachi did. Nor would you expect a 12/13 year old to be Anbu captain, much less join the organization at the age of 10. Nor would you expect a 13 year old kid to be taking on S-Rank missions. Nor would you expect the same kid to become a missing-nin at that age and join/hold his own in an organization like Akatsuki filled with S-Rank criminals. He progresses through things quickly. Looking at that image, it's not like he could just stand there and watch the war, he'd be in the way. I'm sure that he took out a few people with kunai and shuriken when he had to or could at least hold his own against a few shinobi, even at that young age.
