I stumbled around for a little bit with this one. The path to the Python executable must be set in the configuration settings for the Atom autocomplete-python package, and the part of the path with the executable filename must include the
.exe filename extension.
For example, the full path to my WinPython executable is
C:\Users\UserName\WinPython-64bit-18.104.22.168Qt5\python-3.5.3.amd64\python.exe. Entering this path exactly as shown here worked.