Yes, light can indeed transmit more data than radio. That's why fibre optics are the backbone of the internet. While his technology sounds impressive, he fails to address some of the obvious flaws with this system.
First of all, visible light cannot pass through objects. Which indeed does make for a more secure connection, since data transmission is limited to the room you're in. However, visible light needs a clear light of sight between the transmitter and receiver. Meaning that mobile devices would not work if they're in a pocket or purse, which is where most people keep them when they're not in use. So you still need radio, otherwise you wouldn't be able to receive texts or phone calls in the dark.
The second issue is how the smartphone communicates with the base station. Nobody's going to want their flashlight or display on all the time. That's going to drain the battery like crazy, and would also be very annoying. Once again it would also require a clear line of site with the base station.
Third is the limited effective range of visible light. Smartphone flashlights and displays aren't bright enough to function effectively outdoors using this system. Especially in the daytime. So at best you'd have one-way communications. Meaning that you'd still need radio for two way communication.
It's actually pretty stupid what he's trying to sell when you actually sit down and think about it. There's just too many compromises to be made in order for it to work for mobile, which is the crux of his argument. This video came out almost four years ago and the technology still hasn't hit mass market. Probably a good reason for that.
Now, where a system like this would work is in static environments like an office. A lot of office buildings leave lights on all the time for security. So it makes sense to harness that wasted energy for data transmission. Since desktops aren't moved around much, you could easily set up a network without having to run CAT5 cable all over the place. At home, they could be used to transmit data to smart TVs and other devices that tend to sit in one spot. I believe some companies have been working on developing such systems. Marketing it though as an alternative for mobile devices is just too far fetched.