Oh, PLEASE--they have been making missiles spin in flight since the days of Congreve rockets (War of 1812). If this article makes so simple and fundamental an error, how accurate is the rest of it!!!!
The scheme referred to here was to make the ICBM as shiny as possible and spin the upper sections so as to spread the heat of the laser as much as possible.
Another possible countermeasure is to release a metallic cloud or fog from the nose of the missile so as to reflect as much of the beam as possible.