I think this is the whole article:
http://www.rsc.org/suppdata/c6/ee/c6ee02923j/c6ee02923j1.pdf
From a brief skimming, they aren't looking at the round-trip efficiency of hydrogen, just efficiency of the electrolysis part.
They're probably drawing from the heat produced by the charging and discharging of the battery itself to make the electrolysis more efficient (hydrogen is also one of the losses many batteries experience during charging, including this type). It's an interesting idea, but it's far off from practical implementation and without any criticism or repetition it's sensible to be skeptical.
It's also not clear how long these batteries actually last when they're being topped off all the time with impure water; I don't know how tolerant their chemistry is.
https://en.wikipedia.org/wiki/Nickel%E2%80%93iron_battery
Due to its low specific energy, poor charge retention, and high cost of manufacture, other types of rechargeable batteries have displaced the nickel–iron battery in most applications.[8]
So it doesn't retain charge well. That's one of the reasons they got as good results as they did; I think they just charged them up and released the charge right away.
When it overcharges it's just going to be a crude electrolysis device (which will probably shorten battery life).
If you have a few sunny days, then a few cloudy days or even weeks (as it usually is), you're going to see a lot of loss.
This is potentially fine for day/night variation, but you're still going to need to start up power plants for a rainy week.
NiFe has a low specific energy of about 50Wh/kg, has poor low-temperature performance and exhibits high self-discharge of 20 to 40 percent a month. These disadvantages together with high manufacturing cost prompted the industry to stay faithful to lead acid.
An extra 10% loss in a cloudy week would be typical.
As to the cost: that is a serious issue that can't be brushed under the rug "build a wall" style.
The weight is not an issue for such an application, so that's fine.
