Yes, you do need a degree. However you react in this artificial situation in which you are grouped up with seven stranger has no bearing on your performance as an engineer. Furthermore, if you had a degree in psychology and wanted to perform an experiment like this you would need to seek approval from an ethics committee and they would turn down your request because the experiment is fucking stupid. Whoever devised this "IBM Asshole Test" is the real asshole here.
The test wasn't to determine your performance as an engineer, it was to see if you demonstrated bad behaviour working in a group under pressure. You could be a great engineer and I'd still pass you up if, in this test, you were rude and abusive, or impatient and condescending to the rest of the group.
