Do you have a minion.log? The minion0.log is for the old version of Minion. I'm running 10.11.6 on a MBP and its running fine here so I don't think its due to 10.11.6. Hopefully you have a minion.log and there is an error to go by.
You could try starting Minion from command line and see if there is an error in your terminal...
Code:
open /Applications/Minion.app
If nothing happens there try loading it from java maybe?
Code:
java -jar /Applications/Minion.app/Contents/Java/Minion-jfx.jar