How can I use a Python script in the command line without cd-ing to its directory? Is it the PYTHONPATH?

I think you're a little confused. PYTHONPATH sets the search path for importing python modules, not for executing them like you're trying.

PYTHONPATH Augment the default search path for module files. The format is the same as the shell’s PATH: one or more directory pathnames separated by os.pathsep (e.g. colons on Unix or semicolons on Windows). Non-existent directories are silently ignored.

In addition to normal directories, individual PYTHONPATH entries may refer to zipfiles containing pure Python modules (in either source or compiled form). Extension modules cannot be imported from zipfiles.

The default search path is installation dependent, but generally begins with prefix/lib/pythonversion (see PYTHONHOME above). It is always appended to PYTHONPATH.

An additional directory will be inserted in the search path in front of PYTHONPATH as described above under Interface options. The search path can be manipulated from within a Python program as the variable sys.path.

http://docs.python.org/2/using/cmdline.html#envvar-PYTHONPATH

What you're looking for is PATH.

export PATH=$PATH:/home/randy/lib/python 

However, to run your python script as a program, you also need to set a shebang for Python in the first line. Something like this should work:

#!/usr/bin/env python

And give execution privileges to it:

chmod +x /home/randy/lib/python/gbmx.py

Then you should be able to simply run gmbx.py from anywhere.

You're confusing PATH and PYTHONPATH. You need to do this:

export PATH=$PATH:/home/randy/lib/python 

PYTHONPATH is used by the python interpreter to determine which modules to load.

PATH is used by the shell to determine which executables to run.

PYTHONPATH only affects import statements, not the top-level Python interpreter's lookup of python files given as arguments.

Needing PYTHONPATH to be set is not a great idea - as with anything dependent on environment variables, replicating things consistently across different machines gets tricky. Better is to use Python 'packages' which can be installed (using 'pip', or distutils) in system-dependent paths which Python already knows about.

Have a read of https://the-hitchhikers-guide-to-packaging.readthedocs.org/en/latest/ - 'The Hitchhiker's Guide to Packaging', and also http://docs.python.org/3/tutorial/modules.html - which explains PYTHONPATH and packages at a lower level.