The error message reads: "Error unpacking jar files. The architecture or bitness (32/64) of the bundled JVM might not match your machine."
Unpacking JRE ... Preparing JRE ... yEd-[version].sh: bin/unpack200: [...] Error unpacking jar files. The architecture or bitness (32/64) of the bundled JVM might not match your machine.
Usually this problem happens for 64 bit systems because the installer uses 32 bit Java internally.
Make sure you have the official Sun/Oracle Java installed, then "install" yEd manually (see also here: The yEd Linux installer aborts with an error message. What can I do?).
Alternatively, you can try to install 32bit compatibility packages for your linux distribution. E.g. for Ubuntu install ia32-libs.
The yEd Linux installer aborts with an error message. What can I do?