That error message means that you are trying to run yEd 3.16.1 with Java 6 or Java 7 instead of Java 8 (version 52.0 is the class file version for Java 8). This also explains why yEd 3.15 still works - 3.15 is compatible to Java 6, while 3.16.1 requires Java 8.
Did you install yEd from the Mac OSX disk image (yEd-3.16.1_with-JRE8.dmg) or from the Zip archive (yEd-3.16.1.zip)?
How do you run yEd? I.e. do you manually execute "java -jar /path/to/yed.jar"?