Looks like you can email that alias (resign@broadcom.com) as instructed, and they will adjust your termination date and pay out severance. As it reads you will forfeit the warn period pay. I would wait until 1-2 days prior to your new start date to send this email to allow BC to get that alias working.
Also remember to read the instructions on sending in your laptop and other relevant equipment.
If any others interpret this differently please comment here to help each other out. We're all trying to decipher these materials. Many people surely have new jobs lined up. Note that to qualify for severance the documents say you cannot work at another company and BC at the same time.