You don't need a CS degree to be successful but it'll be a lot easier to get in the door.
Most top-tier tech companies (google, fb, twitter, etc.) won't even interview a non-cs candidate for an engineering or product role unless they have incredible (like, you built instagram) evidence of their talent.
It's also a lot harder to skip the degree and still learn what you need. I did, and it's taken me 10+ years of constant curiosity (and tons of nights and weekends) to be on par with my peers who have degrees.
That all said. You gain other skills with a liberal arts or science degree that CS majors don't get. I'm a much better communicator and manager than many of my engineering colleagues, and that has allowed me to outpace them in terms of career growth.