A ridiculous idea.
The article doesn't go into technical details, but it appears this boils down to a compact proton accelerator. Those protons could be smashed into heavy metal atoms, which will release high energy neutrons. Those neutrons could in turn be used to irradiate nuclear waste, transmuting it.
The first problem with that idea is that stable atoms would be transmuted, too. So unless the waste is separated chemically (aka reprocessed), irradiating it with neutrons tends to make matters worse. In some cases, notable cesium, isotopic separation seems necessary. But if you assume reprocessing, you might as well stuff the components to be irradiated into a reactor, where the actinides act as fuel and some waste products will transmute away.
The second problem is the ridiculously low efficiency of such an accelerator system. Carlo Rubbia has been talking about the concept (ADS, Accelerator Driven System, also called Energy Amplifier) for something like 20 years, and even he only envisions supplying comparatively few neutrons to a subcritical reactor. But a barely subcritical reactor isn't all that different from a critical reactor, except you can turn it off by turning off the accelerator instead of by moving a control rod.
In short, this is another guy with a solution (the accelerator) looking for a suitable problem.
(For the record, continuous recycling of actinides is a good idea that turns "the waste problem" from an unsolvable million-year problem into a manageable 500 year problem. Transmutation of iodine and technetium may be a good idea, too, because these are the only long term radionuclides that would leach into water.)
Edit: names are difficult