Hi,
I'm not sure if I get you right because I didn't read your reference...but as war as I know the Vgs-Vth is the "excess gate voltage" of a MOSFET device.
So if this is the case if you wnat V* to be 200mV and if Vth is 300mV, you need to set the Vgs=500mV...
You can find more information in Allen Hambley's book "Electronics", chapter 5.
For short-chanel fet I think that there is a scaling coefficient in the equation but I don't know exactly. You can use as a reference Behzad Razavi's book "Design of analog CMOS Integrated Circuits", chapter 14.

Hope this helps!

Gergana