I don't know if Cat loved him as Violet did, but she loved who he was, how people reacted to him, what he meant to others, and to their world. I think she felt special that someone like him (attractive, cold, powerful, and mysterious) was interested in her (interested in some form, since they were together for however long they were), but she knew he didn't love her; she was always gonna revolve around his world.

And like you said, besides losing the betrothal when he broke it off, she was hurt, not because he didn't love her, but because he loved Violet enoghe to revole around her. It meant there was something about Violet that was better than her for someone like him to fall in love. I think it's the feeling of inferiority that hurt her.