It's not really possessiveness is it? He's still her brother and he feels that he failed to protect her from Klaus(from his POV). The lover in him is further disgusted that their intimate moments i.e. the spankings, dom/sub names took their root in pedophilia.
They didn't. That's not how it works.
It's right there in the game, too; reread Haley's words leading up to the sex scene. She wanted her brother to take her and make her his from an early age, certainly predating Klaus ("I was just a kid, remember?").
As for whether or not it's possessiveness...until this update he's only had two chances to express his feelings about Haley and other men. He seemed to be generally supportive of Jack and slightly confused by Haley's obvious rejection of her boyfriend, and when he talked her out of flirting with Adriana's husband there's no indication that it was because he was jealous, only that he thought it was a terrible idea. (That he can end that encounter by getting a hand job from Adriana kinda highlights my point about potential hypocrisy, though.)
But now, in the space of 12-18 hours, he's done it repeatedly. In the car he outright states that Haley and Nick didn't matter
then but it does
now, and his reaction is surprisingly aggressive. He's clearly somewhere between uncomfortable and upset when they encounter Nick, and Haley's teasing doesn't exactly improve matters; only her rejection of his invitation to the bar seems to. In the bathroom scene at the school he directed most of his negativity at his ex, but he still felt compelled to ask Haley if she'd joined in and seemed uncomfortable with her then-pending answer. And then there's the postcoital scene.
Compare this with the MC's expressions of sexual jealousy elsewhere. He just shrugs off Diane's "lets keep this casual." He lets Alana calling out another name roll off his back. The one and only time he gets anywhere near the person he's suddenly become is when he forces Adriana to treat their most recent sexual encounter more seriously by taking
him more seriously. (All of this, of course, assuming you've chosen to go ahead with those scenes.)
I think it's pretty well established that Haley believes the MC 'owns' her... or at least desires it to be so:
What is not established yet, is the MC's feelings on the matter, since he never explicitly states his acceptance of that concept. We may infer things one way or another, but he hasn't said anything about that yet.
He goes back and forth. Sometimes he slides into the dominant role quite easily, as with the spanking scene, ordering her to come to his room, or in the early stages of the sex scene when she's first getting undressed. The Adriana scene I just mentioned was another expression of dominance, and both times he pushed Sandra's limits were at least dominance-adjacent. On the other hand it sometimes seems to frustrate him...at times explicitly (like when they're getting ready to have sex) and at other times more indirectly, as when he was trying to make Haley understand that he wasn't going to unilaterally decide whether or not they were going to have a sexual relationship.
It's too early to tell, but he may be someone who enjoys d/s roleplaying but not actually being a Dominant, which is why he reacts differently depending on the situation. Whereas, as you say, Haley's very, very serious about this. This is yet another point of potential conflict; it's one thing to be into spanking, leashes and ball gags, or being called Daddy when it's all for fun, but Haley's an actual sexual submissive and she's going to need him to be committed to his role or she's not going to get what she wants.
) And in fact she narrates the entire experience right from that script; she's responding to him in some sense, but she's really responding to the way she's always seen it in her head. She's as much having sex with an image of her brother as she is her actual brother.
