How much does a PhD degree matter in today's startup world/tech industry?

I don't think that formal education is an important factor in success of a startup. After all, when you're steering the ship, there's no one to withhold raises because of your lack of education; it's all about the merits of your product and your marketing.

If you think a PhD will give you the skills you need to run a successful startup in the most efficient way, then you should probably do that, but I don't think the PhD distinction is going to do much for the first intention of "run[ning] a startup".

However, some of the big players do put a lot of clout into that kind of thing. All of the anecdotes I've heard indicate that Google, Amazon, Facebook, and others weigh formal qualifications heavily in the case of an anonymous resume. Many of Google's job listings state a preference for an MS or higher.

I think at high profile companies like that, where thousands of unsolicited resumes are received every day, strict formal educational requirements is a necessary way to pare down resumes queued for review.

At lesser-known companies, the qualifications are generally much looser, mostly focused on a demonstrable background with applicable technologies. You don't need any formal education at all for most jobs in the industry, just demonstrable experience and positive reviews for your past work.

I can only speak for myself of course, but I have no formal qualifications and it hasn't stopped me from launching two successful start-ups or working in the industry at CTO and Technical Director level. That said, I have now made the decision to return to further education (I'm taking a different direction). Point of case: I'm currently working as the technical lead for a biomedical institute, managing a team of seven bioinformaticians, all of whom which have PhDs.