You can read it here:
If you choose to actually read it, you will find out, that there are absolutely no extraordinary claims in there.
1) The energy density is stated relative to the amount of pure Lithium and they need about 8.5Wh per gramm of lithium or about 120 Gramms of Lithium per kWh. Which is in line with ordinary lithium batteries. The difference is merely, that lithium-ion batteries mostly consist of anything but lithium. The graphite anode alone is about 10 times as heavy as the lithium it can store.
2) The concept is a Lithium-Sulfur battery, in which the cathode consists of lithiumsufide. This is a well known and established concept, that has some major problems with liquid electrolytes, as some of the polysulfides that form as the cathode releases lithium ions are actually liquid themselves. Which causes parasitic discharges and damages in to the cathodes. This battery has a solid electrolyte.
It is also not a panacea. There is a reason why the title isn't "A safe rechargeable battery with insane capacity" but "Alternative strategy for a safe
rechargeable battery". It is a new approach to develop a practical battery with this technology and it looks rather promising, but far from perfect. If you read it, the battery cycled for 1000 hours. Where each cycle consisted of 10 hours charging and 10 hours discharging - so it releases its energy rather slowly (as well as taking it up). There were also only some 40-ish cycles in total.
I don't know who wrote the article or whom they interviewed to write it. But they never read or understood the article that Goodenough actually wrote.