Once, I worked in a government data processing department. The best director we ever had was completely non-technical and knew it. He got his information and technical education from us. He trusted us, tried to get us what we needed, and things in general worked well.
On the other hand, consider Steve Jobs. When he rejoined Apple, some analysts were seriously saying it was time to liquidate the company and give the proceeds to the stockholders. Now, it's the biggest computer company around in market cap and revenues, and last I saw edged Microsoft out in quarterly profits.
Jobs did it by deciding what he wanted, realizing what of it could be accomplished, and doing everything possible (including bullying) to get his people to produce it. His success depended a lot on his taste and ideas, and his ability to realize what was impossible and what wasn't quite.
For a company to do reasonably well compared to past performance (like Microsoft; very big but very limited growth prospects), it has to have a competent CEO. To perform spectacularly, like Apple or Google or Facebook, the CEO needs to have a vision, and the vision needs to be largely achievable. In order to pull that off, the CEO needs to have a good idea as to what's possible and what's not. That will usually require some technical knowledge, even if not actual proficiency.
For running a high-tech company that's already established, a non-techie can be CEO with no problems. For spectacular success, it really helps to have a CEO who's technically aware. I'd be really, really reluctant to invest in a high-tech startup that was run by non-technical people.