is just the start. He starts with "water boils at 100 °C, right?" which I expect you'd agree with.
He then _continues_ to work out that, despite the simple definition, the everyday-life _experience_ of boiling water is nowhere near as simple. Why is it not so simple? Because, details.
Which is the point of the whole essay.
> gets the details of boiling water wrong
Can you give an example of a detail he got wrong?
> The rest of the exposition is unnecessary and wrong given the true definition
His _goal_ is to explore the details of the everyday-life experience of "boiling water" in the everyday sense of "boiling" and show how it's more complicated than what the simple (technical) definition would lead you to believe.
Part of the trouble is that the word "boiling" means two distinct but related things:
1. Heating liquid so much that all of it transitions to gas (your technical definition, restated to be a verb form -- "boiling water", a gerund phrase, cannot be a temperature, as you proposed to define it)
2. Heating liquid so that _some_ of it is transitioning to gas, while the rest of the liquid can be used for cooking
The second sense is what people actually mean when they say "I'm going to boil some water" or "Is the water boiling yet?"
As an aside: I love the bubbling patterns of water as it heats, and it's actually a useful skill in the world of tea-making (especially in the gongfu tradition) to estimate the temperature of water based on the amount and size of bubbles. Nowadays I use a temperature-controlled kettle, but in the past I would get by with a clear borosilicate glass kettle and paying attention to the details, which is fun and rewarding in itself—if far less precise.
The author gets the details of boiling water wrong. He commits a fairly common error: using his experience of a practical and common phenomena to make/guess a technical definition. The technical definition of boiling water is simply the temperature beyond which liquid water will not go (let's ignore super heating- too much detail!). The rest of the exposition is unnecessary and wrong given the true definition (although could probably be reworked from a cooking perspective)