I'm not sure that the speaker really directly addresses the point of disagreement with Anderson.
The kenosis (Phil. 2:6-8) is not Jesus emptying himself of divine attributes, which omniscience and omnipotence are. Jesus performed miracles: healing the sick, raising the dead, calming storms, etc. And unlike the apostles, he did so on his own authority.
What Jesus emptied himself of was his divine privilege. He laid aside his divine prerogatives and took the form of a servant. If a king were to become a servant, he would not thereby lay aside his humanity; and Jesus, by becoming a man, did not lay aside his divine nature. In the Incarnation, humanity was added to deity, diminishing neither.
And as the following verses say (9-11), because of Christ's humility and obedience in going to the cross, those same glories and privileges that were rightly his, by virtue of his being deity, were again bestowed upon him. Again, in Christ's temporarily laying aside his exalted status, nothing was lost of his nature.