The things Obito did were inexscusable, Naruto did not say he forgave him or excuse what he did in any way. He told him in either 652 or 653 he would have to make up for what he did. Just like Naruto told Nagato he did not forgive him for what he'd done but he accepted his change of heart because he realized the killing and the hatred had to stop somewhere.
Naruto operates on an emotional level, as did Hashirama, since the were both Ashura's transmigrant. When he was pulling the bijuu out of Obito he got to see inside Obito's heart so much so that obito was unnerved by it. Naruto could see into his heart because they were both jinchuriki. He saw his past he saw his dreams and aspirations and realized that Obito had been a good person at some point in time. He also got to see Obito was regretting his actions. Naruto saw Obito was having second thoughts and started the TNJ.
That was enough for Naruto. He saw Obito's change of heart and accepted it. As with Nagato he made the decision that killing and hatred wouldn't solve anything and if he could turn an enemy into an ally he would rather do that instead of kill them.
As for Naruto complimenting him, he might have gotten carried away with the emotion of the moment or it might have been a response to anger at BZ who was putting Obito down. I will wait for the VIZ translation as Manga Panda and Manga Stream are different.
BZ has been manipulating people for possibly thousands of years and is the cause of the current events and not only shows no remorse at all, but even bragged about how he used the Uchiha. So I would think Naruto felt that someone so evil should not mock someone who was trying to redeem themselves.
Also when Naruto tried to heal Obito he did realize that Obito was dying and he couldn't save him. So did Sakura when she touched him. Obito did save Naruto's life twice and was helping the alliance. It could be that Naruto wanted him to die with dignity since he was attempting to make up for some of what he did.