If you have local tournaments that are close to you then it'll be a lot easier to convince them than if you have to take like a 3 hour coach ride or something to get anywhere. Plus it depends on what degree of independence your parents allow you in general, and just generally how open-minded your parents are.
But I'd try to emphasise the social aspect of it. If they see games as a waste of time because they believe the game itself has no inherent value, then make the game incidental. And you'd be telling the truth; the social aspect is a huge part of things. In a lot of ways the game is just one of many possible methods of bringing people together and nurturing a community. I've made friends with Melee. I've gone on road trips with those friends to stay the weekend at the house of some guy I'd never even met with like 10 other Melee players for a tournament, and been totally accepted and had a great time. I went to a different country on the other side of the world where I had no friends and I was immediately able to hit up the Melee people there and hang out with them out of nowhere. I met my boyfriend through Melee.
Many gaming communities (and fighting game communities especially, which have an interesting history that explains this) have this kind of strong, pretty much intrinsic social element, and that's not something you'd expect if you're someone's dad who has never been exposed to this kind of stuff and goes into it without an open mind, with the presumption that games are just toys, you know? And if they only see you practicing alone it's easier to miss the point; you're practicing alone because you ultimately have to play someone else, as with basically all sports or any number of other hobbies.
And beyond that you could push it a bit more and say that regardless of the activity, practicing and getting good and analysing your results and competing and stuff is valuable in general. That might be a little harder to convince them of, since if they believe gaming is a waste of time they're focusing on how a game has less obvious "intrinsic" value than some other hobby such as a sport (which would improve your physical fitness). But compare it to something like art; unless you're making it big art is a hobby you're going to put a lot of time and money into just for personal pleasure, yet people are far more likely to consider that a productive hobby, despite gaming being similar, mostly just because gaming still has a stigma about it. Melee is probably cheaper than buying art supplies too lol; you just need a controller, a Wii, and a CRT you could pick up from the side of the road (I literally got mine like that), and that's it apart from travel costs. And, like art or sports, practicing Melee is a way for you to develop a lot of skills that are valuable to have as a person. The skills required to compete and think critically about yourself to improve are transferable to anything.
Melee has helped me in general. It's been an activity I can use to support myself when I'm feeling depressed or anxious (honestly, basically the only thing that kept me remotely part of reality and gave me anything to do other than lie in bed and stare into space was Melee for a while, and that really helped me get through things), and the skills I've learned to facilitate improvement have helped me both learn other things more efficiently and mindfully (it's worth specifically mentioning that it applies to schooling), and helped me deal with my mental health issues similarly.
Plus it's just fun. As long as you're balancing the rest of your life well enough that should be an argument in and of itself. If you're doing fine at school then you can afford to take this time to relax and do what you enjoy.
There are plenty of videos which express this kind of stuff that you can show them if they'll bother to watch them but I can't think of any offhand.
