約束の問題じゃねーんだ
This isn't a matter of promise.
サクラちゃんとの約束がなくなっても 関係ねーよ
It doesn't have to do with with your promise, Sakura-chan...
even it's still valid or not.
I am not sure if I have translated very well the last part in eng. The core of Naruto's speech is that whatever the promise to her is still ongoing or not, all this didn't have to do with that. Naruto wasn't trying to save Sasuke because of that promise, as thought by Sakura for mistake at the first. Anyway I just took a liberal way there because it wasn't so esplicite in original.
Thanks so much, I really appreciate it a lot! :-)