Yes, that's why everyone with a CS degree has made millions of dollars. This is offensive to everyone that makes games.
>You merely need somebody with a computer, a good idea, and the ability to make a game
However, the talent required to pull off a quality game and the time it takes are huge and only grow exponentially. That in recent years we've got a couple of indie games that were successful, that's only because on mobile devices the expectations for CGI quality are for the moment low. Plus, with these app stores, the budget required for marketing has decreased, if you're lucky enough to have your app featured.
And while you can create indie games for the desktop and be successful, as Minecraft shows, the expectations for quality CGI are much higher and so it takes an insane amount of creativity to fill the blanks.
Now, of course, Zynga games are not really on the same level as what id Software or Blizzard are releasing and you can certainly picture yourself pulling off games of the same quality, as Zynga games are nothing special, except for the social-network effects.
However you shouldn't underestimate the effort required to build a game from scratch. I consider it to be by far one of the most challenging fields in software development, as not only it requires great feats of engineering, but it also requires creativity and design. E.g. developers by themselves can barely pull it off without the help of a good artist that can draw.
... but the barrier to success on the scale of FarmVille or Draw Something is very high. That's when a company with massive amounts of money that can be spent to hire game developers and market to users has a distinct advantage.
Game design is not a science. Try enough times and you will create a hit.