What you read on their website today is probably true of a contract written today, but doesn't have any meaning for any previously written contract. The contract is what it is, and if it lacks provision for a transfer, then it is not.
If the seller told you the warranty was transferable and that was instrumental in your buying decision, then you may have recourse with the seller if that proved untrue, but that's between you and the seller.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL