I was a PM at a bigger company (~350) before jumping into startup land. After being the CTO and de-facto PM for a couple startups, I've had an idea that probably needs some vetting:
I think when you're still small, most typical PM functions should be distributed instead of centralized, with a manager getting in the mindset of managing people who are 10-20% PM / 80-90% engineer or designer.
While the overall product/business strategy and business requirements should be owned by one or a few founders/officers, I think as many people as possible in an early stage web/mobile product company should have most of the general skillset of a PM. Highly specialized talent might be an exception if you're creating a sophisticated product or have unique interface goals. But the general PM skills -- mockups, basic design principles, writing stories, writing requirements, managing a story/requirement from creation to deployment -- should be universal while you're small.
The inflection point goal at web/mobile startups is getting MVP after MVP out the door until you've pivoted or iterated your way to a good-enough product for a good-enough market. (Or good-enough product for a specific customer.) It's an all-hands-on-product affair.
With this in mind, I think the early CTO should be a hybrid of engineering talent and director of product management. Or perhaps depending on skillset a separate person (another co-founder or the person you thought should be the first PM) is that director of PM and the CTO is more like a lead architect. The point is that rather than doing all the product management or all the VP Engineering stuff, this person (or two) manages a team of hybrid engineers/PMs, retaining some important overall product and architecture decision-making responsibilities, but empowering and helping designers and engineers employ basic PM skills individually or split among a small group such that the person or small group owns more process for a feature.
This makes sense to me, but at a startup assuming that the CEO is the lifeblood of the idea for the company (as s/he should be) aren't they essentially the PM manager that you describe here? I guess this is a moot point, but we're obviously only focusing on a startup that is heavily technology focused.
What about one where the pudding is actually a process or physical commodity and the technology portion is merely an extension of this?