How important is extracurricular activities in college application?

I am not … into sports… It’s not just what I like doing. I like watching some basketball games, but that’s it.
I am pretty good in music, though I play clarinet, guitar, and piano.
I am not good at arts.
In this case, what exactly do I do to make myself stand out? Certainly I can’t do it with extracurricular activities.

Although, I am really, really good with computers. I know how to program in dozens of programming languages. Also, I have been exposed to couple of theoretical computer science theories like complexity theory and computability theory…etc.

Or should I get involved in some olympiads like IOI, IMO, IPhO, etc?

Or should I just stick with my passion and keep going with it and not do anything else?

It depends. Are you applying to schools that care about ECs? Are you applying to hyper-selective schools? If you are headed to your State U, then quit worrying about ECs and focus on your grades and test scores. If you are applying to places were ECs matter, then you already have two interesting and important ones, which is all you need (depth not breadth). It’s really about what you do with them and how you describe them in your applications. You like music and programming - those are your ECs. Don’t both doing olympiads if that’s not your interest - or sports or arts or anything else. Find ways to expand upon those two ECs that you care about, in ways that fit who you are and you will be fine.

Examples: You are good with computers and know how to program. Do you do programming for any organization? Have you programmed anything interesting? Do you do it for money? Are you self-taught or did you take classes somewhere? You are good in music - do you perform? compose? take lessons? teach? build instruments?

Don’t undersell yourself just because you aren’t in clubs or other organized activities. You don’t have to ‘prove’ that you love these things with any outside validation (although it’s nice if you’ve got it). Just share what drives you and in what directions these interests have taken/are taking you.

No one cares that you play sports or not. No one cares if you like to watch some basketball games especially.
Music is a good EC.
No one cares that you are not good at arts.
Computer programming and related is a good EC and/or academic supplement.

Some colleges are strictly by the numbers and don’t care about ECs. Most colleges actualy. Just the top colleges who want leaders and to build leaders care, care and smaller privates where they wants students who will help create a vibrant campus community. If you don’t apply to those you don’t have to worry about it. If you do, then deepen your commitment to your current EC and see what you can do to be a leader or otherwise make an impression in that area. If you might get something out of oympiads, sure get involved.