There were many LOST characters who had special gifts or talents, like Charlie and Daniel who had musical talent. But there were very few characters that were directly told that they "were special."
From recollection, these characters were once called "special:"
Claire was told by Aussie psychic Richard Malkin that Aaron was special.
MIB was told by Crazy Mother that he was special.
Ben told Locke that he thought he was special, as an island protector just like Locke thought of himself as having a special destiny to protect the island. Both men never wanted to leave the island, but did so in a time of crisis by turning the FDW.
Locke was told he was special by his Mother, because he had no father (immaculate conception).
Locke was also told by Richard Alpert that he was special when he was being recruited for a school.
Desmond was called special by Daniel because of Desmond's ability to mentally time travel and harness the island's electromagnetic properties.
Walt was called special by Tom and the Others who kidnapped him. Also, Walt's step father called him different (and dangerous) from his psychic abilities which included killing birds.
One could argue that "miracle babies" would be classified as "special."
Ben was born prematurely in a forest, far away from any medical care or treatment.
Locke was born after a car crash, and miraculous survived in an ICU chamber.
Aaron survived a plane crash to be born on the Island.
Jacob and his brother both survived a shipwreck to be born on the Island.
Alex survived a shipwreck to be born on the Island.
But Walt had none of background of the miracle babies.
Until he literally outgrew his role, Walt was the focal point for the Others.
He had some power or ability that the Others, including Ben, wanted to test or harness.
Walt had psychic abilities as a child. Some believe they were premonitions. Others thought
that he could control events, and cause death (such as various bird deaths). His step father was so afraid of him, he dumped him off to his father, Michael. "Sometimes when he is around, things happen," Brian told Michael. Example, he stopped the rain in order to search for Vincent in the jungle.
Walt also appeared as an apparent apparition: a) his imagine leads Shannon into the woods, who is then shot and killed by a startled Ana Lucia; b) he appears before a dying Locke who was shot by Ben and tells him to get out of the Dharma mass grave because "he has work to do." Now, this could have been the work of MIB taking the form of Walt in order to get the 815ers in motion for his "loophole" plan to kill Jacob (for which MIB may have needed Walt off the island -- through Michael shooting Ana Lucia and making a deal with the Others to leave with no chance of returning and then having Locke become his patsy to con Richard, Ben and the Others to lead him to Jacob for his revenge.)
Many theorized that Walt was supposed to be the new guardian. There is no conclusive evidence to support that theory. Walt's name did not appear in the Lighthouse as a Candidate for Jacob's replacement. Jacob never "touched" him.
Some theorized that Walt's psychic kinetic powers would be a weapon the Others could use against Widmore. He Walt thought about something, his mind could make it really happen. Like after reading a comic book on the plane about polar bears, a polar bear attacks the survivors.
But all speculation led to a dead end. Walt was written out of the series.
Was Walt "special?" In the first four seasons he was deemed special in the story lines. But in Season 6, his role brought no insight into the Finale. Walt only appears in archive footage with Locke in the End. Walt's character had no role in the events that led to the church conclusion.
But the mystery leading up to the last season was Why was Walt special? What was the reason or purpose for Walt special traits? Like many LOST questions, we really do not know.