Not really. The first part of the new timing is just for cards that use the “Initiate a Duel” phrase. Then you’re forced to follow the restrictions.
But in this case, you skip the Initiate a Duel step and go to the Resolve Duel step because:
“A duel is resolved during the successful resolution of any triggered ability that instructs players to “resolve the duel,” or that their “character challenges the opponent’s character to a [type] duel.” To resolve a duel, perform the following steps”.
Which is the exact case of Taryū-Jiai. You must meet the pre-dash criteria of the ability, which is “During a conflict, choose a Shugenja character you control and a Shugenja character controlled by an opponent” and then you resolve the post-dash effect of the ability, which is “your character challenges your opponent's character to a glory duel. The winner of the duel's controller resolves a ring effect of his or her choice as if he or she was the attacking player.”
See how that phrase match exactly the phrase in the RR? The same phrase that instructs you to resolve the duel when said phrase is used?
This is exactly what Tyler was talking about during the AMAs, all duels follow the same steps, unless the card instructs otherwise, which is this case.
I’ll admit is not probably as clear as they wanted, at least with old cards. But when we get used to the new framework with new cards, the moment any duel card don’t follow that framework it’ll stand out on its own, and everybody will realize it’s one of the dueling exceptions.