It is a fascinating case, though your article overplays the internet aspect. At issue is not free speech over the internet, but whether intent is required for something to be a threat. Basically, Elonis says he did not intend for his lyrics to be a threat towards his ex-wife, and therefore he did not do anything wrong. The state says that intent does not matter, that if an average person looking objectively at the words would find them threatening, then it is a threat. The medium the threats where transmitted on is only relevant as context.
And I am really torn on that issue. I can see how his ex-wife would be legitimately scared reading those lyrics he posted and feel threatened. However, why should some one be subject to jail time and other penalties because some one else misunderstood his intent? I think for me what this comes down to is when in doubt, you err on the side of the right. Rights are good things, but all can and will be used to do bad things. Westboro Baptist church is a vile group, but they still have the right to free speech and to do vile things which cause distress to others. In this case, Elonis's lyrics where vile and hurtful, but absent clear evidence he actually intended them to be threatening, he should have the right to be vile and hurtful.
Some further reading on the case from the always excellent SCOTUSBlog:
Drawing a line between therapy and threats: In Plain English : SCOTUSblog
And SCOTUSBlog's case page:
Elonis v. United States : SCOTUSblog
