And they have to top everyone. Otherwise they're not alive. You see, they also mostly grew up in narcissistic households and are used to being either the best or useless. So their every conversation is about establishing whether they're the best or at least better than you.
PWC has an interesting post on how narcissists don't want you to be happy for them, just envious of them. It's true.
But they don't seem to really be able to tell the difference. If you admire their achievements / acquisitions when they brag about them, you could be doing it because you want to flatter your superior or because you're genuinely happy for another human being. The difference is beyond them. For them, you're the weak loser if you just say "How wonderful!" or "Congratulations!"
Because, you see, a stronger narcissist would find fault with the achievement / acquisition and this is a risk they take every time they brag about something. You can sometimes sense the trepidation underneath their superiority: Will I win this one? Will my success be attacked? Will I defend it by attacking the attacker well enough? Will I emerge from this as the winner?
You've got to feel sorry for them. Life is a constant battle for them. Support from others is interpreted as their defeat and these losers are immediately discarded as weaklings whose opinion doesn't matter anyway, since they're obviously inferior ("She says she likes my new car, and it must be because she wants to suck up to me because she admires me, which means she's weaker and unworthy of me"). The stronger narcissists who attack them powerfully enough are hated and feared. And they're in constant battle mode. And they're never at ease. And they're so alone.