Zach, I think the key distinction that Piper is making here is between justification and salvation. These terms are not identical. Justification is one of the salvation benefits. It is a key part of salvation (the main hinge, as Calvin would put it), but not equal to all of salvation. Regeneration, adoption, sanctification, and glorification are all part of salvation more broadly considered. The Bible uses the term "salvation" (and its attending verbs) in more than one way. The Philippian jailor asked "What must I do to be saved?" This is the more commonly used biblical definition: the moment when we pass from condemnation to justification by faith alone through grace alone in Christ alone. However, there is a broader definition of salvation that includes all the other benefits of salvation as well. In this regard, read Turretin on the necessity of works. They are necessary in a consequent way, not in a causative way. I use this analogy: if a cannon fires, does it make a noise? Of course it does. An explosion makes a noise. Does the noise cause the cannon to fire? Of course not. It is the inevitable result of the explosion, not the cause of it. Similarly, works are the inevitable result of justification, and in this way only are works necessary. We obtain eternal life in heaven not because of our works, but also not without our works. We hear the word "necessary" and automatically run to the idea of causation. We need to resist doing that. If our works play no part at all in this broader definition of salvation, then we run the very real risk of antinomianism.
Even in sanctification, God's grace comes first, but in sanctification it is an enabling grace that makes good works inevitable. So God's grace works differently in sanctification as opposed to justification. God's justifying grace is declarative. God's grace in sanctification is enabling.
The key point with regard to FV theology is that they mix up the attendant qualities of justifying faith with some kind of causation. The definitional problems hinge around the nature of faith. They will tend to say things like "we are justified by faith/faithfulness." Or they will say that we are justified because of faith's aliveness. That is where they go off the rails. We are justified because of Christ, or on the grounds of Christ's obedience active and passive. It is Christ's righteousness that causes our justification, and/or is the ground of our justification. Faith is instrumental, not causative. Piper very carefully guarded against these errors in the clip by excluding all our works from justification, period. Conclusion: at least in this clip, Piper is not even playing footsie with FV. I might ask a question of him as to the relationship between union with Christ and justification. He seemed to be saying that union is part of justification, a statement I would not agree with. But he is hardly FV here.