The donor of the gift is usually liable for reporting and any applicable taxes when it exceeds the exclusion limits. Not the recipient.
I've not found anything where it says the gift is reportable by the recipient, only the giver, when it exceeds the exclusion amount. Even if the gift exceeds the exclusion amounts, the recipient is still not taxed. Can you show me where the recipient is responsible for reporting and paying gift taxes? At least for federal purposes?
I said reportable, and it is. It’s in the link you posted. The 2018 exclusion is $15K.