To be completely, totally clear: playing a sport yourself is not narcissism. Playing a sport yourself is extremely healthy unless your teammates are all malignant narcissists. Physically moving your body and dealing with real, immediate, definitely-your-business physical problems. Except possibly golf, which is clearly profane for reasons I cannot articulate.
The weird thing about spectator sports is it's largely about allowing the "professional" players to be narcissistic. Which is double-weird because a good sportsman usually isn't narcissistic, because playing a sport is so healthy and nobody can pretend winning is losing.* The final score is not subject to social word games.
*(Players aren't actually dumb (commonly 125-130 IQ) and I think this narcissism angle neatly explains why their interviews are so brain dead: you can't have the players contradicting the role the narcissist sport-watchers are projecting onto them, which means they can't say anything of substance. It would reveal some of their character. The fact national-level sport absolutely wipes you out mentally is merely a bonus; they don't have pretend to be thoughtless in post-match interviews. They are, temporarily.)
It would be super great to be a sportsball hugger or puck hucker if you were a narcissist, eh? Tens of thousands giving you narcissistic supply in person! (Hence the real narcissists are found behind guitars.)
The puzzle with sportsball is it's kind of bad entertainment. Folk get just as excited at concerts, but you can't lose. If risk of loss is part of the appeal, there's casinos. You can buy nearly a dozen movie theatre outings for one evening at the ball game. And, you know, video games. You don't spend more time watching ads and breaks than playing a video game after you've fired it up. Maybe when plays with comically bad costumes were the height of entertainment technology, watching a sports game was competitive. That was a long time ago.
Bad entertainment, unless you're delusional.
Spectator sports is a way for sports fans to reaffirm their own narcissism. By supporting the allegorical narcissism of the players, they normalize giving of narcissistic supply. The fan cheers for the players because you're supposed to cheer for the fan - especially when they're losing.
I shouldn't have to say this, but I probably do: I'm not supporting the idea of abandoning your cooperators if they stumble. (Ref: tit for two tats.) A loss, however, is a loss. It's bad, not good. It's not time to cheer.
A sports fan becomes an identity. What do you actually do? You sit in an overpriced chair, maybe wear an overpriced downmarket vest. It's nothing. Fake identity, especially one you get super excited about, is 100% narcissism.
The narcissist lacks boundaries. To a narcissist there are two kinds of person: someone who is identical to the narcissist, and Others. As long as the players don't accidentally Other the narcissist, they can feel like the player's wins are their wins. You paid for a ticket, therefore you paid your salary, therefore they couldn't win without you, right? Right. The more you paid, the more the win is your win....despite the massive pot belly....
It's not like they're getting wins anywhere else, so the potential win is worth the risk of a loss.
See also: business owners will often show off their wealth by buying a particularly pointless reservation at the local stadium, but they will rarely attend the games. Even if they do, they will invite someone and functionally hold a business meeting. Why? They have money. They get their wins elsewhere.
I think this also explains why fans are so loyal to a particular team. To properly get into character, they Other every other team. Likewise, they feel Othered by that team when they, the big meanies, try to score on their team. To a narcissist, everything is personal. Everything that isn't narcissistic supply is an expression of personal hatred.
Likewise, if you consciously pick an identity off the shelf, it feels fake. You have to "accidentally" choose an identity. In other words you can't just run the numbers and choose to be a fan of the team that wins the most. Or rather, the kind of person who runs the numbers and makes rational decisions is too healthy to be sucked into sportsball narcissism, so they never become a fan.
Parasociality is highly narcissist. Healthy minds find these fake plastic relationships as satisfying as a fake plastic sandwich.
Appearance trumps substance. They're very excited about signed materiel, and not at all bothered that the signing player couldn't pick them out of a lineup, let alone help them with anything IRL. Probably too busy to even say, "Sorry to hear that Champ, hang in there!" if you're having a bad day. Utterly worthless...unless you can wring narcissistic supply from signs and portents.
When they say players are idolized, it should be capitalized. They are Idolized. As a way of Idolizing the fan that "worships" them, because narcissists don't have boundaries.
Egalitarianism: if [epic sportsdude du jour] is great and strong, then, because everyone is identical, the sports fan is great and strong too, see? Indeed they get a little bonus for recognizing how great and strong the player is, rather than turning their nose up at jocks or whatever I will inevitably be accused of doing.
If it were genuinely entertainment, watching the game would be the point. Watching it "live" would mean little. If you couldn't watch the game, the score would be irrelevant. Maybe find out who won for purposes of future drama, but it wouldn't be a big deal.
If the game were the point, then it wouldn't matter if video game versions of the sport had fictional players or even if they were all green space aliens. An offside is still an offside, a goal a goal.
If it were some benign prestige-by-association thing, knowing the score would be enough. Interruptions during play wouldn't be a big deal.
Since it's a narcissism thing, watching it "live" makes it easier to "identify" with the players - to confuse them with yourself.
Since it's a narcissism thing, the self-deception ritual works better if you're not brought out of suspension of disbelief by a distraction or someone cutting across your vision.
Since it's a narcissism thing, it's important to make sure that (as far as you know) you know everything the players know. They certainly know the exact score of every game they play in. (Again, the players aren't supposed to say anything in interviews you don't already know - which is pretty difficult since differing individuals will know wildly different things - unless they say, basically, nothing.)
P.S. The flagrant anti-egalitarianism of sport arena market segmentation amuses me a lot. They don't even pretend to want to make the nosebleed seats feel like chads, there's rules specifically to (mildly) heckle them for being so poor. Also I'd like to know how they recruit thin, attractive, and typically white cheerleaders, since that's so very clearly an EEOC violation. They just kind of get away with it though.