I think that your ECs are very good. Your grades, test scores, and class rigor are also excellent. I think that you are competitive at any university in the US (and many more outside the US).
The point of ECs: You should be doing what is right for you. What is right for you, what was right for me, what was right for my wife, and what was right for each of my two daughters, are five completely different sets of things. That is entirely okay. Also with ECs, whatever you do, you should do it well.
“Top 20 in North America”( presumably among high school players?) in chess is very impressive. I am humbled.
Welcome to engineering, high tech, computer science, mathematics, and chess, and a few other things. This is common.
Three things come to mind here.
A professor who I know once told me that of his academically strongest and most intelligent students, he thinks that all of them have at some point suffered from some degree of depression. “All” might be a bit of an exaggeration. However, this is common.
The medical profession has gotten pretty good at helping people with depression. Have you talked to a psychologist or a psychiatrist? It is worth taking the time and effort to get checked out by a professional. I know a few people who have suffered from some relatively serious episodes of depression, and gone on to be very successful, and with treatment much happier. One option would be to start with talking with a nurse or guidance counselor at school, but it would be better to at some point get to talk to someone who specializes in this. They really can significantly help the large majority of people with depression.
The third thing that comes to mind is that some very highly ranked universities (MIT and Caltech come to mind) can be very stressful. It is not clear to me that this would be the best environment for you. I think that it is worth thinking about what sort of university or college would be the best fit for you. Visiting a few schools might be a good idea. There are lots of excellent professors and strong students and a wide range of opportunities (such as research and internship opportunities) at a very wide range of universities.
I got my master’s at a university that is highly ranked overall and specifically very good for physics and engineering and for my major, which was a subfield of applied math (it was Stanford). The other students in the same master’s degree program had come from a huge range of undergraduate universities. It was rare to find two people who had attended the same university for their bachelor’s. I similarly once tried to recall the ten smartest and most accomplished people I had ever met. I ended up with 14 people and could not reduce the list, and they had gotten their bachelor’s degrees at 14 different universities (edit: I am sure that if there were more than 14 people on the list, there would have been a very high chance that there would also be more than 14 universities on the list). You really can get an excellent education at a very wide range of colleges and universities.
In order to be happy at specifically MIT or Caltech (or perhaps a few other similarly academically challenging schools, probably including Stanford), you need to work very hard, and the desire to do this should come from inside yourself. To give you one example, in the master’s program at Stanford I was taking five classes at once. One class had a homework assignment with five problems. One of the problems took me six hours on a Saturday, from about 11am to about 5pm (then I went to out to dinner with my girlfriend after). Let’s suppose that you similarly spent six hours on a sunny Saturday working on one single homework problem. How would you feel after you finished it? Would you be thrilled that you could do it, or would you feel that you just wasted a Saturday afternoon? If you would be thrilled, then an academically challenging school might be a good fit.
First read the “applying sideways” blog on the MIT admissions web site. Then participate in whichever ECs you feel are right for you.
Top universities want a well rounded student body. This does not mean that every individual student needs to be well rounded. I am pretty sure that some top universities for example have chess teams that would love to have a strong incoming recruit. However, top universities also have strong physics and engineering departments, and they would like strong students also. I am also pretty sure that MIT and Stanford have lots of students on campus who were very good at chess in high school, and some more who were very good at robot competitions, and lots more who were very good at a wide range of other things. I remember meeting someone at the opening reception for incoming international students at MIT who had won a major sailing competition. Again, do what is right for you, and do not worry about what university admissions wants you to do – they want you to have done what is right for you.
Somehow I doubt that John McEnroe had well rounded ECs before he started at Stanford. He had done what was right for him, which was of course tennis, and tennis, and also tennis (and in his spare time, more tennis).
You have already done and are doing an enormous amount.
I think that you are doing very well, except that you should get some help for your depression. I think that you can just keep up the good work, and look for schools that are a good fit for you. It will take some time for you to figure out what a good fit is. That is okay. You have time to figure this out.