That's true, but the main argument made by the website is about the space advantage, so it's very relevant that that space advantage is basically nullified by the widespread use of compression.
If your worry is parsing speed, then JSON not only has battle-tested parsers, but also has SIMD-assisted parsers which can process gigabytes a second on a single core (e.g. https://github.com/simdjson/simdjson). It would take Internet Object years to develop parsers as performant as that, even if it did, by some miracle, achieve wide uptake. So the notional advantage afforded by not having keys on each row is neither here nor there.
And incidentally, as someone who's written a handful of parsers, I suspect that this scheme would not be particularly easy to parse. You need lookahead because of optional fields, as well as maintaining state and a lookup table for mapping positions to keys, etc. I can draw up a quick parser in pseudocode or Python to explain, if you disagree.