I actually assumed levitation was already possible by facing two magnets with the same poles towards one another, but with sufficient weight to keep them from drifting apart completely. If I'm not mistaken, isn't that how some subway/rail systems work? (Particularly one called Maglev?) So how is this better? Wouldn't the levitation achieved from focusing a lens be more limited in application?
Did you read the article? A maglev-type system would be utterly useless in the kind of applications that are discussed.
Anyway, firstly this approach doesn't depend on the use of massive amounts of electricity (ala maglev systems) to maintain the levitation effect. Second, you wouldn't be confined to levitating materials with electromagnetic properties. Third, this can be applied on a much, much, much smaller scale.
There are 3 very quick and dirty reasons why this is better.
January has April's showers
And 2 and 2 always makes a 5
Dreaming up plans for first human levitation device.
Accept the past. Live for the present. Look forward to the future. Robot Fusion
"As our island of knowledge grows, so does the shore of our ignorance." John Wheeler
"[A] scientist looking at nonscientific problems is just as dumb as the next guy." Richard Feynman
"[P]etabytes of  data is not the same thing as understanding emergent mechanisms and structures." Jim Crutchfield