Just because the article-writer is being hyperbolic and calls a laser-sustained fusion reactor a star doesn't mean it has much in common with a real star. Nor, as Christopher said, the containment system anything like that in a Dyson's sphere--quite the opposite. In the reactor, the sphere stimulates the reaction. In a Dyson's Sphere, the sphere collects energy from the star.
Well since you seem to have all the answers perhaps you can explain HOW they intend to collect the energy from this fusion reaction? What will they be using?