Magic Kingdom is not officially "Magic Kingdom Park." Nor is Animal Kingdom.
Regardless, the difference is there's always a word before Park that denotes place. Even though your trash MDE app may read Magic Kingdom Park or Disney's Animal Kingdom Theme Park, do you call it that verbally? Would you ever say "Hey kids, today we're going to Magic Kingdom Park!"? No, because the word Kingdom already denotes place. The word Magic is an adjective.
The difference with Disney('s) Cinemagine Park is that there's no other word that denotes place, so Park must fill that role. "Hey Kids, today we're going to Cinemagine!" doesn't sound right, instead you would naturally include Park in everyday speak.
I cannot think of a single major theme park for which that's the case.