It may be significant that the Platinum package plan is not a
Disney dining plan. It is not available as a ticketless passholder package and it is not available on DVC points reservations. You also can't upgrade a free Disney Dining Plan to either the platinum or premium package plans. For the Platinum you must also book a deluxe resort.
The dining portion operates somewhat like the Disney Deluxe Dining Plan, with the main differences being that there are additional restaurants that accept the premium and platinum plans, and all restaurants (including signatures) cost only one credit per meal.
To book it, you must book a package reservation at a deluxe resort including at least a one-day ticket, and add the platinum dining plan.