You could try the batch set
command to put the drive letter into an environment variable, then use that variable in the NppExec script. To set the environment variable try something like:
set TheDriveLetter=%CD:~0,2%
To use it in the script use:
cd $(SYS.TheDriveLetter)\MinGW\bin\
There is more information in the section on variables in the NppExec documentation.
Notepad++ may itself have some environment variables that provide the drive more easily. You could try here for a list of them.