The sentence "The Software may not be used as part of an automated process." in the yEd Software License Agreement means that you may not use scripts or GUI automation toolkits to run yEd. Only a human user may run/use yEd.
You may generate input files for yEd like GraphML/GML/TGF/etc. in any way you like. E.g. it is perfectly fine to have a cron job that automatically polls a database to generate a GraphML file and then have a human user manually start yEd, open the cron-generated GraphML in yEd, maybe modify the opened diagram in yEd, and finally save or export the (possibly modified) diagram.
You may also process yEd generated output in any way you like. E.g. staying with the above example, lets assume the human user exported the diagram as PDF. It is perfectly fine to have a second cron job pick up said PDF and publish it on a web server.
The important point is that everything that is done with yEd is done manually by a human user.
This clause is a safe-guard to prevent yEd from being misused as a yFiles replacement. Obviously, we do not want our free products to hurt sales of our commercial products.