The correct answer is option 'D' - North-Eastern Railway. Here's an explanation of why it is not recognized by UNESCO World Heritage Site:

Introduction:
- UNESCO (United Nations Educational, Scientific and Cultural Organization) World Heritage Sites are places of outstanding cultural or natural significance.
- These sites are recognized and protected by UNESCO to preserve their cultural, historical, or natural value for future generations.

Darjeeling Himalayan Railway:
- The Darjeeling Himalayan Railway, also known as the "Toy Train," is a narrow-gauge railway located in the Indian state of West Bengal.
- It was built between 1879 and 1881 and covers a distance of about 88 kilometers.
- The railway is famous for its unique engineering features, including loop lines and zig-zags, and offers breathtaking views of the Himalayan mountains.
- In 1999, the Darjeeling Himalayan Railway was inscribed as a UNESCO World Heritage Site due to its cultural and historical significance.

Nilgiri Mountain Railway:
- The Nilgiri Mountain Railway is a charming toy train that operates in the Nilgiri Hills of Tamil Nadu, India.
- This railway connects the town of Mettupalayam with the hill station of Ooty, covering a distance of 46 kilometers.
- It was completed in 1908 and is known for its unique rack and pinion system, allowing it to climb steep gradients.
- The railway was recognized as a UNESCO World Heritage Site in 2005 for its outstanding engineering and scenic beauty.

Kalka-Shimla Railway:
- The Kalka-Shimla Railway is a narrow-gauge railway in the Indian states of Haryana and Himachal Pradesh.
- It was built in 1903 and covers a distance of about 96 kilometers, connecting the city of Kalka to the hill station of Shimla.
- The railway passes through 102 tunnels, 864 bridges, and many picturesque stations.
- In 2008, the Kalka-Shimla Railway was inscribed as a UNESCO World Heritage Site due to its historical and engineering significance.

North-Eastern Railway:
- The North-Eastern Railway mentioned in the options is not a specific railway line or route.
- It is a zone of the Indian Railways that covers northeastern states such as Assam, Tripura, Manipur, Nagaland, etc.
- While the North-Eastern region has numerous scenic and picturesque railway routes, there is no specific railway line referred to as the "North-Eastern Railway" that has been recognized by UNESCO as a World Heritage Site.

Conclusion:
In conclusion, among the given options, the North-Eastern Railway is not recognized by UNESCO as a World Heritage Site. It is important to note that the other three options, namely the Darjeeling Himalayan Railway, Nilgiri Mountain Railway, and Kalka-Shimla Railway, have all been acknowledged and protected by UNESCO due to their cultural, historical, or engineering significance.