Commercial li-ion battery energy densities have continued to improve during that time period, including the commercial introduction of cells with silicon anodes. Of course, silicon anodes are a new tech, so there's a great deal of room for improvement, which probably won't come close to "maxing out" for a decade or more.
Of course, that said, this article is your typical fluff piece following the guidelines of fluff science reporting.
1. Present an oversimplified version of one technology challenge that may or may not address the biggest issue and certainly doesn't address all of them - but don't mention that.
2. Introduce an outside-the-establishment loner with a passion - or at least someone you can try to present as "outside the establishment" and glaze over anyone who helped him.
3. Loner gets a "vision" based on some everyday activity
4. Present their solution and make it out to be a huge revolution that will certainly solve all our problems - if they can only get corporate backing / funding!
I think these sort of articles hurt the image of science because people read them, think "OMG, all our problems are solved!", then when everything's not solved afterward, fail to trust science in the future. For example, in this case, the most important element to improve is the cathode, not the anode. And cathode improvements are less common and usually less major than anode improvements. There's also tons of different anode improvements out there in various stages of research. Pretty much all of the silicon ones get way better than graphite or amorphous carbon.
That doesn't mean that this isnt an important paper - actually, from looking at it, it looks pretty good. It's just not "all that".
BTW, anyone know how credible this journal is? I see it's hosted on Nature.com but not part of Nature, and I tried to find an impact rating for it but couldn't.