There's a lot of reasons Ryo could have to join a tournament, that wouldn't go against what he had been taught.
Frankly I don't know why people are making a big deal out of the supposed morality that Ryo is suppose to have. If it leads to him improving his martial arts abilities, which inturn will help him beable to defeat Lan Di when he finds him, how is that against Ryo's character at all.
Also just because someone joins a tournament, doesn't mean they're doing such to show off. Fighting against other strong martial artists, can help one grow greatly as a martial artist, plus I don't see why such has to only take place in a do or die situation(A tournament is a nice controlled environment, fair, and clean, no to the death or anything).