Lithium batteries in a Tesla (and just about everything else consumer-grade) are designed to burn rather than explode - they can produce an impressive jet of flame, but this is contained and safely vented from the battery vessel. Just like gasoline-powered cars, they catch fire, but don't (usually) go boom. They are also capable of failing in a controlled manner - lithium-polymer cells are contained in sealed pouches which expand during failure as the gas pressure rises. So long as the pouch is not breached, the battery is a very low fire risk, and is akin to a leak in an air-powered system - a low-energy release that does not harm people around it.
Compressed air, however, does explode out of any weakness in its fittings, often with no warning. Catastrophic failure of a weak joint, coupled with a pressure difference of several atmospheres, can turn any ejected fittings into artillery shells. There's plenty of videos of air compressor explosions on YouTube. Yes, this is considerably rarer than a lithium battery fire, but don't forget that lithium batteries are relatively new to the scene. Compressed air has been in use for hundreds of years and the dangers, despite being understood, are still present. A lot of them stem from human overconfidence, and the attitude of 'eh, one more bar can't hurt, can it?' Even a small workshop compressor operating at less than 10 bars can cause life-changing injuries to anyone present should it fail. I'd argue cleanup from these types of failures are much, much messier than lithium fires.
The comparison to lithium batteries is pretty accurate because unlike gasoline, a spark is not necessary to start the fire. However, a lithium battery fire can generally be spotted by temperature rises before it becomes dangerous. Failure of a pressure vessel is much harder to predict. Just a tiny manufacturing defect in a square-centimetre of a pressure vessel can create a weak spot that'll be the first place to fail as it comes under operating pressure, or cycled repeatedly.
Don't get me wrong, I'm interested in off-the-grid living and had not considered compressed air as a power source until reading this, but I do feel the article skips over the safety aspect of compressed air. There's a reason many of the fittings are only sold to industries - used improperly by amateurs, the pressures they're discussing could be fatal if something goes wrong. My advice to anyone reading this article is to fully understand the dangers of compressed air before building something like this.