Which parks truly qualify by these metrics? Disney, Universal and Efteling...? Europa and Phantasialand (haven't been to either but from what i've seen)?
In recent years, all of the above. Efteling have only recently been creating more cohesive lands, but the park always had the underlying themed identity of fairytales, folkelore and myths. What sets Phantasialand apart from the rest is that themed areas like Klugheim have worldbuilding elements that you kind of have to research so as to better understand what they are. Taron, for example, I originally thought was themed to a dragon flying through a village, but it's themed to an ancient device created by the villagers to harness the raw energy of the land, which is meant to provide Klugheim with power.
Phantasialand is mostly about creating environments where their guests can escape into, environments that are full of character, but the storytelling isn't as in your face. Disney are (or were) perhaps the masters of crafting clearer stories and fully cohesive themed environments that best fit the overall themed identity of their parks.
As far as the UK goes, Chessington and Legoland are the country's most authentic major theme parks if we're to go by these metrics. At the end of the day, theme parks are a 360 degree non-linear storytelling universe, an art form which was pioneered by Walt Disney and the original Imagineers at WED Enterprises during the development of Disneyland, which set the benchmark for what would become the themed entertainment industry.
Thorpe has theme park like elements.. but it's not an authentic theme park. It's just like other amusement parks that dabble in themed experiences. It stood a strong chance of becoming a theme park back when it was An Island Like No Other, but this has been ditched in favour of a very Amusement Park identity of Feel Good Thrills. Perhaps they finally realized that in order to fully return to the park's original theme park roots they'd have to spend an awful lot of money at making the Island themed identity truly cohesive across the park so as to remedy the brand identity crisis.... the park genuinely did not know what its identity was from one attraction to the next.. horror warehouses galore...
Hyperia would've been a strong entry to the adventurous Island identity, but we simply have a stylized hyper coaster, which isn't a bad shout for an amusement park catering to thrill seekers predominantly. Authentic theme parks mostly cater to a wider breadth of people, families, capturing the imaginations of children while making adults feel young again... that's the ethos of Walt Disney and it's adopted by the parks mentioned above as well as many others like Parc Asterix, Toverland, new parks in development like Hossoland etc.