Well, yes and no. This article isn't about unemployment, it's about jobless claims. While jobless claims are tallied the way you describe, unemployment numbers are derived from a monthly poll:

http://www.bls.gov/cps/uiclaims.htm

Those numbers also probably understate the problem, but not for the reason you mentioned; the official unemployment numbers do not include people that are underemployed or those that have stopped actively looking for a job.