I'm going to address this in two parts. First will try to explain Pinkie Pies element, the second how her ( and all the elements ) play their part in relation to each other.
1. In one episode Princess Celestia was addressing the mane six, and how they had shown proficiency in their respective element during their adventure. ( it was at the end of the episode) she said "each of you have shown me how much you represent ( or grown, I don't remember exactly) each of your elements" she then went on to use a synonym for each element. Like "integrity" for AJ and "gentle spirit" for Fluttershy. Anyway, when she got to Pinky she said "enthusiasm". Until then I had always wondered about laughter as an element. But when Princess Celistia refered to it as enthusiasm, I got it. She is enthusiastic about everything. She makes their adventures fun. She always has a song or a joke, or cake, or balloons, even if that song or joke falls flat (or comes across as just comic relief) to us, the other ponies seem to enjoy it. And if they don't she will keep trying. It sometimes seems like the more she fails the harder she tries, which more often than not, results in people (and ponies) becoming annoyed with her.so, yeah, try to think of "laughter" as also being "enthusiasm.
2. I've always seen the elements (and the ponies) as kind of a metaphor. Like if you know someone that has loyalty, kindness, honesty, generosity, and they make you laugh (and if you possess those qualities yourself) then that friendship is magic. So, you can have a loyal, kind, generous,, honest friend, but If they don't make you laugh, or If they aren't fun. That person likely won't be your best friend (...and therefore not magic). It's that best friend magic that weaponizes rainbows. Like the song at the end of Twighlights Kingdom says. Hope that helps.