Try too late
This concept was already tried, though in a slightly different manner, in the movie The Wizard. It was a pretty stupid concept then, and it remains a stupid concept. In theory, it's just as normal or strange as any other sport; it's just that with video games, you're using your brain more, and your movements are much more subtle.
The problem is, as this article points out, watching other people play video games is incredibly boring for most people. Most people would rather be playing the video games than watching somebody else play them. Contrast that with physical sports, in which the spectators usually have nowhere near the abilities of the professionals.
That's not to say there aren't a great number of people who do enjoy watching others play video games. I'm sure there are. But there aren't enough to make it profitable. People will gladly pay upwards of $400 to watch the NHL Stanley Cup finals or the MLB World Series. People will not be willing to pay anywhere near that to watch other people play video games. I'd go so far as to say that most people who would be interested in watching a video game competition probably don't even have $400 of disposable income without robbing their savings account (provided they're lucky enough to have anything in savings in today's economy).