The batteries being talked about are 18650s, which is mentioned pretty clearly in the article and apparent from every single picture of batteries in it. This makes sense, because the vast majority of laptops sold across the world use a set of 18650s as their batteries. These are also the form factor of batteries being used in current Tesla powerwalls (though I believe they will also switch to the 21700 form factor as production of that ramps up).

18650s are just as safe as any other battery chemistry in everyday use, but they're a high energy lithium cell. In particular, if you do bad things to them, they may light on fire. It's not that hard to take appropriate precautions to avoid that, and reasonably sized lithium-ion battery fires can generally be put out with a standard househould fire extinguisher.

It also appears the community is collaborating to spread good information about powercell design to avoid/manage fires inside the units, in the unlikely event a cell starts a fire. If the container for the powercell is designed correctly, it can contain a complete unit burndown: https://electrek.co/2016/12/19/tesla-fire-powerpack-test-saf...

In short, you're overestimating the risks and underestimating the level of safety attainable with these products.