Good question! The Unique Ability is a thematic variation, whereas the Crucial Element is a character trait. As you said, the Unique Ability is what gives the Main Character the capacity to solve the Overall Throughline, but think of it as a thematic connection. Whereas the Crucial Element is a behavior that character exhibits which makes them relevant to the story. It's either the OS Problem, Solution, Symptom, or Response, depending on the Main Character Resolve and either Growth or the OS Outcome.
Here are three examples I picked from the website:
The Babadook--Change, Success. Amelia's Crucial Element is her Desire. Because she wants her family situation to return to normal, her personal struggles against her memories of her husband manifest into the Babadook. Her Unique Ability, though, is Circumstances: despite her failing Senses grating on her and driving her insane, her love of her son helps her to recognize when her evaluation of her life has gone awry. By coming to grips with her understanding of her circumstances, she can finally banish the Babadook for good.
Othello--Change, Failure. Othello's Crucial Element is his Conscience. Othello wants to be a good husband and an upstanding citizen, but Iago twists that desire into "righteous" fury, precipitating the events of the play. Othello's Unique Ability is Approach. We see this really strongly at the start of the story: Othello's soft Approach at the trial is what convinces the court that he hasn't enthralled Desdemona with African witchcraft. But time and again we see that if Othello could just reclaim that Approach instead of playing right into Iago's hands, none of the events of the story would happen.
Back to the Future--Steadfast, Stop. Marty McFly's Crucial Element is Dyscontrol. Marty's Drive is Hinder--he must hold off his mother's advances long enough to see his parents brought together--but he's brought into the story because of his freedom from the laws of time. Marty doesn't act using the same social customs as the people of 1955, which leads to all sorts of mischief. Marty's Unique Ability, meanwhile, is Openness. Because of Marty's more modern attitude, he can use methods and ideas from 1985 to give his father a "happy ever after." (These two came out pretty similar, so let me break it down. Marty's interaction with the story is Crucial because he's free from the confines of 1955 society, but he's able to bring success to the OS because of his adaptability to this new world--his Openness.)
The Incredibles--Steadfast, Start. Bob Parr's Crucial Element is Ending. Bob's desire to end his purgatorial existence and return to a place where his heroism is welcomed leads him to recklessly Trust Mirage and Syndrome. His island utopia allows him to pretend that the superhero stigma is gone. His Unique Ability is Threat. The only way for Bob to bring back the love of superheroism is to reveal the threat Syndrome poses to humanity, effectively expanding the island to all the world. (Again, Trust is what makes him effective in the story: Trust in Mirage, Trust in his family, Trust in his own desire to see the world made right. But his perception of and focus on Threats is what helps him reach Success.)