If your parents are bona fide residents of Puerto Rico and don't have US income, then they are not subject to US tax laws. Instead, they are subject to Puerto Rico tax laws, and they will have to check the PR laws to see what the requirements are when giving gifts.
As a gift recipient, assuming your parents are not US persons for income tax purposes, then I would think you do need to report gifts over $100,000 on form 3520. (If you send it in and the IRS doesn't need it, they'll let you know.) No tax is owed as the recipient of a gift, it is just a requirement to report the transaction.