You still need very pure water or you poison the process. Where's that water coming from? How do you collect the gaseous hydrogen? You still need to liquify it and all the emrittlement and cryogenic issues are still there.
Even if hydrogen gas is free, it makes no sense as an energy carrier for cars.
They don't collect the gaseous hydrogen in the electrolyzer; they soak it up with a "liquid sponge" ("a recyclable redox mediator (silicotungstic acid) " according to the article's abstract. In principle at least, hydrogen could be stored and transported in this form (a liquid sponge soaked with hydrogen).; the hydrogen can be catalytically released (wrung out of the liquid sponge) when needed. Whether such a system could be built with a practical size, weight, and cost for use in vehicles is another matter.