Were the believers Paul persecuted still Jews under the Law?
Yes. Those believers whom Paul persecuted were Jewish believers, and they were still Jews under the Law. They remained under the Law, as Peter also remained a law keeper at that point in Acts. This was before the later turning point to the Gentiles.
Les teaches that Paul recounts his own experience of persecuting Jewish believers, but they were still Jews under the Law. That is the point being emphasized. Les further notes that when chapter 10 is reached, Peter is still a law keeper, showing that these early Jewish believers remained law-observant. The bigger context is the turning point in Acts, where Saul of Tarsus is called as a chosen vessel to bear Christ's name before Gentiles, and also to kings and the children of Israel. Les explains that Paul would suffer many things for the sake of that name, and was finally martyred because of it.