Well I am completely convinced. Linux office applications are clearly (clearly!) better than commercial suites. /s
To the point of the article, despite the last point saying the practice of using old laptops is a hack, they spend most of the article brow beating anyone that doesn't follow suit or agree with them.
Some laptops are awesome and can last for many years. These are often (not always) laptops aimed at enterprise/institutional buyers...like many ThinkPads. They are designed to be serviced and have readily available parts lists and service manuals. Internally they're fairly prosaic which makes servicing more practical. Others are just generally well built and don't have a lot of moving parts to even fail.
Everything else is just shit that can't be easily serviced and is always falling apart. It's expensive and frustrating to keep such laptops longer than a few years. If you can't avoid buying one you're better off properly disposing of them than fighting with them. If you do have a laptop with good/serviceable hardware it'll easily keep working well for years.
I think the point of software is the author's strongest point. If Linux/FOSS is a feasible platform for your work and you have a productive workflow you're going to have a much easier time with Linux on an old machine versus Windows. Even the fastest moving rolling release Linux distros change far less than just Windows 10's semi-annual releases. The requirements also aren't going to change much if at all.