No, you are not allowed to distribute yEd with a Software Distribution Tool.
The sentence "The Software may not be used as part of an automated process." actually covers both of your interpretations. You are neither allowed to use parts of yEd in other tools and applications nor allowed to distribute yEd automatically to multiple clients.
If you are interested in installing yEd on multiple clients in an automated fashion, please contact the yWorks sales department by email (firstname.lastname@example.org) to negotiate a custom license agreement.