Not really, the term honor killing is used to refer to an act of murder in retaliation for someone doing something that is seen to "shame" a family or group thus by the family or group killing the person they are demonstrating they hold complete contempt and absolutely no feelings for this person and are under the impression they are regaining some kind of honor that they feel was lost by the person acting in the way they did.
This is a murder fueled by a sense of jealousy and regret that a relationship had ended, not really what the term honor killing is usually used for.