The article is light on details, but it claims they're storing the hydrogen as a solid - not as a gas. Solids are generally about a thousand times more compact than a gas.
That's hardly a revolutionary thing - there are hydrogen powered cars on the road and those don't use hydrogen as a gas either. Those cars don't make much sense compared to lithium, but mostly only because there's almost nowhere in the world you buy hydrogen for your car. That's not an issue if you're producing your own hydrogen at home.