I disagree. I think this episode made it clear that Emma does have magic. That is what August said. He needs to get Emma to believe so that he will help him.
He didn’t say he needed her to believe so she could help him herself, he said he was going to get her to believe, which is a key step in her breaking the curse and potentially bringing them back to FTL, which has magic. Nothing actually says Emma herself has any magic at all.