I wrote a lot of software before I ever took a CS class in college. The only things you'll get from a CS degree are the ability to prove problems are NP-Complete, learn how to do Dynamic Programming, reductions from one problem to another, Linear Programming, Graph Theory, and a bunch of other math tricks (random hashing, fast modular exponentiation, The Gauss multiplication trick, etc.). You don't need any of that to write a Chrome Extension.
If you need software to scale to hundreds of millions of users, then you probably need people who have CS degrees to think about your hard problems and how best to optimize them and which ones have no polynomial time solutions for all inputs (problems to be avoided or worked around somehow).
I can do RSA by hand (on small messages), quickly tell (with only pencil and paper) what 2^1027 mod 3 is and do Euclid and Extended Euclid by hand to find multiplicative inverses (in one pass). But I can write code that runs pretty well, too, and I can do that with or without a CS degree. So can most people.
If you need software to scale to hundreds of millions of users, then you probably need people who have CS degrees to think about your hard problems and how best to optimize them and which ones have no polynomial time solutions for all inputs (problems to be avoided or worked around somehow).
I can do RSA by hand (on small messages), quickly tell (with only pencil and paper) what 2^1027 mod 3 is and do Euclid and Extended Euclid by hand to find multiplicative inverses (in one pass). But I can write code that runs pretty well, too, and I can do that with or without a CS degree. So can most people.