When Jareth first saw Sarah he was drawn to her for her creativity and imagination. She believed in creatures like him or could accept such creatures as potentially being real, something rare in the modern world. She was a beautiful and innocent child. He was drawn to that innocence, perhaps because her pure dreams were such a stark contrast to how he saw himself and his own reality. Jareth seems perfectly miserable as The Goblin King but Sarah was full of hope and fantasy and ambition. Her love of theatre and her creativity. So much potential that he could never have of his own (though it does require creativity to build and maintain a Labyrinth such as he has).
As Sarah went into The Labyrinth Jareth became drawn to her will. A will as steadfast and strong as his own and in a mortal girl. He was amazed by her tenacity, her refusal to be defeated. Her cleverness and cunning to get through his Labyrinth. The more frustrated he became at his inability to defeat her and the further she got the more he wanted her. Perhaps (because The Labyrinth was an externalization of his own personality and soul and she was solving it) he felt she was getting to know him better than anyone else could as she was getting to know herself.
In the ball room he sees her, not as a child, but as a woman. He uses her dreams against her but in reality he's molding her dreams into his own. Maybe that's why Moppet in Return to Labyrinth has blonde hair. She's not entirely Sarah's dreams. She's Sarah's dreams and Jareth's. Though admittedly other ablations don't have the same hair as their original source. When Jareth sees her in the ball he wants to seduce her. He wants to rule her, to have her. Maybe even to be ruled by her. 'Love me. Do as I say and I will be your slave.' Somewhere around this point he decides he doesn't want an heir (Toby) as implied in the novelization and confirmed in the Return to Labyrinth manga. He wants a queen. 'For what good is a kingdom without a queen to share it with.' (Return to Labyrinth Volume 2).
Jareth knows what love is. Sure he goes about things wrong and sometimes confuses love with domination but the idea of being in love does not evade him. He talks of unconditional love in As the World falls down. 'But I'll be there for you as the world falls down...'
He doesn't want any harm to come to Sarah. 'You didn't hurt her, did you?' he asks Mizumi in Return to Labyrinth Volume 3. For all he's done he's afraid of physically hurting her. Even when she was in his Labyrinth Jareth never allowed any real harm to come to her. If he had left her in the oubliette he would have had guaranteed victory but instead he sent Hoggle to take her back to the start? Why? he says 'She'll soon give up when she realizes she has to start all over again.' But in that same breath he's pretty much admitting to us, the viewer, that is is giving her the chance to start all over again. She can either give up or try again but either way he's rescuing her from the oubliette whereas if he left her there he would have had certain victory. This was mercy. Jareth lies to his minion, and possibly to himself, about his motives but Jareth is a clever character. He must have known that if he had left her in the oubliette he would have won. It's Jareth's own act of mercy that was his undoing.
I think Jareth also suffers from what I call 'The Little Mermaid syndrome.' (Not to be confused with the real medical condition of Mermaid syndrome where a child is born with the legs fused together). By little mermaid syndrome I mean Sarah represents the world Jareth longs for but, so long as he is Goblin King, he can never really be a part of.
David Bowie felt that Jareth rather reluctantly inherited the title of Goblin King and that he would rather be down in SoHo but he's not. Sarah is not just the innocence he wishes he had but also she was human, of the human world. A world he longed to be a part of. This added to what drew him to her.
As Sarah refuses to be defeated so does Jareth. The more she resisted and rejected him the more fascinating she became to him. The more she resisted him, the more he wanted her. But the desire to win the game for her heart was only a small part of it. She was mortal, innocent, cunning, clever, beautiful, and stubborn, her boldness, her bravery, her creativity, her strength of will and her tenacity, her refusal to be defeated, her defiance- it frustrated and intrigued him.
I think he always wanted to either replace Moppet (Sarah's dreams) with new dreams of him or he wanted to control her dreams in such a way that Sarah's dreams would long for him and still long for him when and if rejoined with Sarah. I think Jareth wanted to be wanted in return.
He went about things all wrong and is confusing domination and submission with love but in his own weird way I am certain Jareth does love her, truly love her. I think Jareth just needs a good wake up call to experience what truly means. Then he and Sarah can truly be together.
He no longer represents the aspect of Sarah that she needs to renounce. His purpose to the story has changed and that stage of her life is over with. So maybe now it's time that Jareth must change in order for him and Sarah to both have their happy ending finally.