Perhaps, but also how much of that love depends on the ‘loved ones’ acting in a way that is wanted/expected vs loving them for who they are? How many of these people see their love as transactional, like withdrawing college funding if the kid declares an undesired major?
Loving someone as an extension of yourself is an entirely different thing for a narcissist.
I would add that what OP stated is built into the reason as well. It’s an okay episode, the main problem being that you had to accept the ridiculous premise of talking entirely in memes. Fast forward a decade and the joke very much is that it’s not as ridiculous as it first seemed.