Alibaba is a business that leverages the web to make it easier and cheaper for suppliers to find buyers and vice versa. An older version of this is perhaps a physical market, or a convention, or some kind of club or association, or simply your rolodex of business contacts. The guy that started Alibaba recognised that the web could bring together and match buyers and sellers on an entirely new scale, and at a very low cost: good for users, and good for building a huge company.
He didn't need to be a tech guy to recognise this. His business is _not_ technology. His business is one of the oldest, and most important of all businesses: introductions.
Of course, had he been a tech guy he could have maybe built a website. I don't know his background, but if he had one or more of the following - decent degree, cash or connections he probably didn't find it too hard to raise some money to hire some guys to code the site.
A tech business, I would argue, would be one developing or selling technology. I don't know - designing computer chips, or writing specialised compilers for example. For this kind of business, then yes you need to be a technologist - you won't be able to understand your product otherwise. But simply utilising technology maketh not a technology company.
So with this definition, absolutely - you do not need to be a techy guy to start one of these businesses (e.g a web-based business). In fact if anything, I reckon it's better if you aren't: technologists often spend way too much time stressing about and optimising the underlying technology, when actually what they need to be worried about is the business model that the technology is powering.
Edit: so an example of a "tech" business that isn't really a tech business: an e-commerce store. Let's say you just wanted to set up an online store to satisfy the increasing demand for ridiculous office/executive toys. Do you need to be a tech guy to do this? No: what you need is a sound understanding of your product lines, the market size, your route to market & sales channels and so on. In terms of setting up an online shop there's a million providers who'll set this up for you with custom designs, transaction processing and everything else you'll need to get started - just as there are all the other providers of services that you might need - legal advice, accounting, payroll, inventory management, CRM etc etc.