Hello Jo,
The formula is given for a free LC oscillator. Generally speaking, oscillation frequency depends also on Rs of the coil and cap equivalent series resistance. It also depends on the driving V(t).
When RpMIN/MAX are changed, the driving pattern in LDC1000 is changed as well. This changes oscillation frequency.
Unfortunately, I cannot go into great details regarding methods of driving LC tank, as it is TI IP and cannot be disclosed to public.
In practical applications it is not important to know all of these details, as RpMIN/MAX settings are fixed, and you will observe a change of Rp and or L(oscillation frequency) as a function of your parameter of interest (distance, position, angle etc) Then you have a 1-to-1 correspondence between your parameter and Rp/L and you get the value of the parameter based on on Rp/L measurements.
I hope this helps.