People making these sorts of statements at work would potentially get into trouble because in some countries we have law against harassment at work and creating a hostile work environment.
This situation is more like a bunch of dudes going outside someone's house on the public sidewalk and screaming obscenities. Whether or not it's a direct threat of imminent harm or not, it seems unlikely to end well for the screamers.
Except standing outside their house and screaming the contents of the tweets would surely fall closer fulfilling "true threat" doctrine than tweeting from hundreds if not thousands of miles away.
How is the teenaged girl, at whom many of these menacing tweets are directed, supposed to know where these men making menacing/threatening/disgusting remarks are?
How is she to know or understand that they're not next door, or down the street?