Like @bbbisho mentioned, I guess with a degree, it does carry some weight considering all factors in you actually go through the whole structured education (Endorsed by University's name on it) (most employers want certain warranty, certainly not all).
Sadly, the reality is, not every person is Mark Zuckerburg/Steve Jobs, we can look up to them as aspirations, but do need the reality check as well. Time opportunity plays an important part too. Not to dismiss their legends (no offence), but it could be some other people, some other time, some other stories goes with the name of Brian, Milos or Daniel. That's a direction to look for (I hope).
Nonetheless, I think it all depends on why you started all this journey, what to you want to achieve at the end of it, if you want to make a job out of it (plus point: if coding is your passion), then go all out for it. Focus on getting better everyday. Eventually, your work/projects themselves will tell the story.
Last one, your coding skills itself needs to be compatible with the complexity of the job (regardless of whether having a degree/ not). It's a matter of how convincing are you without a degree. How? Through your portfolio (people can have a look/comment), through verbal communication (tell them what you know/ what direction you want to dwell further).
Often times, I have an admiration for those who are self-taught. It is not easy journey. Yes, there are people ready to help (thank you), but you still need to be actively look for answers for the questions you have. It's an active learning where the real motivation stems from being curious, being interested, being passionate. Down side, it's time consuming. That makes me appreciate how and why certain education system is there, it's structured, with ready/reachable educators, but you have to pay the price. Nevertheless, too much of everything produces graduates who don't even know what they want to do with their degrees.
TLDR I guess I've just typed an essay. Just hope that this reply shines some light.