Reading Commications of the ACM (most recently, [1]), there's been an ongoing problem getting enough people into computer science programs (in large part because of the broad fears of "outsourcing"), and the projections are that EVEN MORE graduates will be needed through 2020. [2]
So yes, many times yes: This article is completely and totally wrong. And as adrianhoward says, it's the same sentiment that my parents chided me with back in the 90s, and that I hear all the time from people who imagine that the silver bullet is just around the corner that will make it so that we need fewer rather than more programmers. (FWIW: My degree is in "Cognitive Science", the "other CS", and I haven't had problems getting jobs when I've wanted one.)
And as an aside, if you look at the graph with yellow and brown bars about 2/3 of the way down [2], getting a job where math is the primary required skill looks like a slog (looks like about 2x as many math grads as math jobs), while in order to hire people AT ALL, companies are going to have to ignore whether they have a computer science degree, because there are nearly 3.5x as many jobs in CS-related fields as there are graduates in CS.
Based on these numbers it looks almost inevitable that we'll see echos of the "You've put together a web page? By yourself! You're hired!" dot com boom, just because it will be so hard to hire anyone at all.
So, while the story was cute, its premise is FUD that has a chance of scaring people away from CS at precisely the time that we need more people in CS. OK, end rant.
[1] http://cacm.acm.org/blogs/blog-cacm/148620-hot-job-market-fo...
[2] http://cs.calvin.edu/p/ComputingCareersMarket
[edit: typo]