And they want it heard in Chicago, IL, since that is very the sole employee of Lodsys has residence?
Is the texas court system known for ruling in patent trolls, like Lodsys, favor?
1. http://www.technologyreview.com/communications/16280/page1/
Basically, you've got it.
Recent legal precedent in the USA makes it easier for someone receiving a demand letter like this to go straight to court, rather than waiting to be sued themselves. The biggest advantage is that by doing this, they get much more latitude in picking the location of the trial, which can be beneficial both in saving travel expense and in terms of jurisdiction. The Times is asking the court to find that they don't infringe, but is also asking the court to invalidate Lodsys' patents, which would also stop them from suing anyone else.
You can generally only file suit in a location where both parties have a demonstrated business presence. The Times publishes nationwide, so they presumably picked Illinois for the reason you mention.
The East Texas federal courts are believed to have a bias in favor of patent-holders in IP cases, and are known for processing cases quickly. So, it's popular for patent trolls and others to file suit there to get an advantage.