A PDF document 'NX1201_mp01_Measurements' can be found in the extracted 'nx-12.0.1.mp01' package which covers some information related to this new Measure command.
I surely read that PDF. It doens't answer all questions though.
What about the old 'Points on curves' measurement? How to duplicate with the new Measure tool?
Using the new Measure command, just pick two points on the curve. NX will display two values; Minimum Distance (associative) and Points on Curve Length (non-associative). To get the value from Points on Curve Length to the previous dialog you can either Right click and copy the value from the Points on Curve Length dialog, or check the option in the Settings called "Send Results to NX Console" to copy/paste the value as required.
Note that this workflow using the old Measure method was also non-associative.