Only a subset of IntelliJ, the IntelliJ community edition has been released as open source software. The page that you linked to describes a special license of the "Ultimate" edition (which is not open source), that they are specifically giving for free to people who promise that they will only use it for writing open source software for non-commercial purposes.
According to the FAQ, the new open source version of IntelliJ is available under an Apache license.
To clarify:
The community edition of IntelliJ is available under the Apache license, which means you can use it for whatever purposes you want, including writing proprietary, commercial software. It also mean you can modify the code of IntelliJ yourself, sell modified versions of it, anything like that, as long as you abide by the Apache license.
The community edition does not have all of the functionality of the ultimate edition. It only has some of the functionality; for instance, it has support for Java and Groovy, but not Python or Scala. But the community edition can be used for any purposes you want, as long as you follow the terms of the Apache license.
The ultimate edition (which includes extra functionality as listed in their comparison) normally costs money. However, they are also offering the ultimate edition for free to people who promise that they are using it for non-commercial purposes for an open source project (I have no idea how they would actually enforce this, but that's beside the point). I believe this is an offer that they've had since before they released IntelliJ community edition as open source software; as a way of helping out open source development, without giving away everything to everyone.
So, go ahead and download the community edition, and use it for anything you want, from developing free software to developing commercial software to modifying IntelliJ yourself and selling it.