It is Baptist theology. NCT is not new (although it is being defined more than in the past). There is just renewed interest and it is being re-articulated.
Where it stands out is in its approach to Scripture. It is a rejection of Covenant Theology and Dispensationalism, but retains covenants and dispensations as presented in the text of Scripture (interpreted in light of the New Covenant).
This may help with the Law issue you brought up. (I'm reading these sites as well):
Because the Old Covenant law, including the Decalogue, has been fulfilled in Jesus Christ, New Covenant Theology denies that the Old Covenant law, including the Decalogue and its so-called “moral law”, is binding on New Covenant believers today. Yet, as the special revelation of God as fulfilled in Christ, the Old Covenant law, including the Decalogue, continues to inform behavior in the New Covenant.