With quotations, support this claim: because Othello loves Desdemona as an extension of himself, his destruction of her is a destruction of himself?
When Iago first arouses his suspicions about Desdemona, Othello says about his wife, “But I do love thee! And when I love thee not / Chaos is come again” (3.3.91-92), foreshadowing his demise at the end of the play. This passage also suggests that his life and reason depend upon his relationship with her, which is a form of narcissism that you allude to in your question. As his jealousy grows, he says “I’d rather be a toad / And live upon the vapour of a dungeon / Than keep a corner in the thing I love / For other’s uses” (3.3.274-76). Here he indicates that Desdemona is for his use but not that of others, and to “share” her would be less than human. This sort of possession indicates he has no sense of boundaries between himself and his wife, that if someone “uses” her they “use” him as well. With this view of his wife, it is no wonder that when he kills her he must kill himself as well, for he is figuratively dead as soon as she is literally dead. This is why he says, “For in my sense ‘tis happiness to die” at the end of the play (5.2.287)