Suicide is always a complex issue with many factors combining to put a person in a position whereby they feel that they have no alternative.
It is dangerous to simplify this and say "she killed herself because she was being bullied online" because the majority of young people who are affected so severely by online bullying have underlying vulnerabilities which make the effect of the bullying worse. For example, Megan Meier, who committed suicide in 2006 following MySpace bullying and humiliation, was already an incredibly vulnerable young person who had been on medication for depression for some time before she died.
To answer your specific questions:
Why do teenagers take the Internet so seriously? Because young people do not differentiate between what is the Internet and what is real life. To them, the Internet IS real life. Popularity is no longer measured by the number of friends you have in the playground or whether you hang out with the 'cool' kids, but by how many facebook friends you have, how many likes your latest status got, how many 'kiks' you have and how many people ask you questions on Ask.fm.
Is it because they are attached too much to the internet? No, it's because the Internet is an integral part of their lives.
Are they trying to escape real life by building virtual worlds? They may be looking to 'fill a gap' in their offline life by building up a large number of 'virtual' friends to share their secrets with in an anonymous environment where they are judged only by their number of friends, not by looks or social status.
Is there any study research on this? Lots! Forget academia, look at media literacy surveys and interviews with kids about their social media lives including this one by McAfee: http://promos.mcafee.com/en-US/PDF/lives_of_teens.pdf