The terms of the deal seem pretty straight forward and are as follows:
If you click on the link it will take you to https://www262.americanexpress.com/business-card-application/raf/200248-CCSG where you can log into your AMEX account and enter the names and emails of the friends you want to refer. Your friends must reply to the offer through the special link they receive and if approved your account will be credited within 8 weeks. You can receive 7,500 Membership Rewards points ("Referral Bonus") for each new Platinum Card application you refer resulting in an approved account, up to a maximum of 55,000 points per calendar year. This offer has a pretty long expiration date and is good as long as you submit your referral(s) by 11/10/2017 and your friends apply and approved by this deadline.
I've written extensively about the American Express Platinum card previously and it remains one of my favorite cards despite its rather hefty annual fee of $450 per year.