I agree that random tweets will be of dubious value. Other ways of engaging in social media (blog posts, Google+ posts, etc) do help showcase your communication skills. It doesn't mean that using those communication channels is a requirement, but you typically have limited interaction points during the hiring process to illustrate your communication skills. Think of blog posts et al as a communication "portfolio" you can use to help prospective employers get a larger preview of what they could expect from you.
I don't mean to come off as dismissive but the article seemed to be talking about communication within a team or with customers and users in a face to face environment. Being able to post on a blog well is not going to get you very far talking to project owners/users to understand business problems. I think social media has an extremely limited usefulness when it comes to determining how well someone can communicate within a real world face to face business environment. I would rather rate a potential employee's ability to communicate on the 15-30 minutes I have to talk to them rather than their social media footprint.