While this first proof of concept is important, significant obstacles remain to make such white lasers applicable for real-life lighting or display applications. One of crucial next steps is to achieve the similar white lasers under the drive of a battery. For the present demonstration, the researchers had to use a laser light to pump electrons to emit light. This experimental effort demonstrates the key first material requirement and will lay the groundwork for the eventual white lasers under electrical operation.
The thing they made is probably best thought of as nano-interleaved resonator cavity for a laser diode (which needs to have certain band gaps to emit the light). Apparently for this proof of concept, they actually had to excite this nano-structured cavity, with an actual laser. These nano-structures couples the energy to desired tunable optical wavelengths which are nano-interleaved and thus allows emission of "white" light from the laser diode structure.
As far as I can tell, the breakthrough is to manufacture these nano-structures (nano-wires or nano-sheets) on the same substrate near each other (nano-spaced). To do this they developed a ion-substitution process which allows them to build the nano-wire structure with one material with certain lattice constants and later replace atoms to create a different lattice constant (changing the resonant wavelength of the structure), This alllowed them to make "blue" which generally so different than "red" that it previously needed to be fabricated with a different structure (making it hard to make nano-structures next to each other).