Locked out of my phone as the touchscreen isn't working I have a LG Optimus G. Some parts of the touchscreen doesn't function.

I wish to retrieve the media content from my phone. Nothing more. So, hard reset is not an option.
I can't use a mouse over OTG as Optimus G, "doesn't support it". 

What are my options?

USB debugging is on, but is on Charging mode. Hence, my predicament.
You say USB debugging is on. Is your phone is already "paired" with certain computers - that is, it it set to automatically allow USB debugging from certain computers? Usually the answer is yes for your personal computer(s).

Assuming this is the situation, you can easily ADB shell to tar/gz any folder(s) you want and "ADB pull" the tar/gz file to your computer.

Another option that you might want to explore is the Vysor application (currently for Chrome), that allows remote control via ADB.