Because your parents do not have cellphones, Google will conclude that it doesn't know a better way to authenticate them and they get to keep their existing (poor) security. As the article eventually explains.
If you would like your parents to have better security for these accounts, I commend Security Keys. Unless your parents aren't together any more, or are just really fervently independent, it's probably fine to buy them one each, but with the suggestion that they both enroll both keys. This way when Parent #1 loses the Yubikey you bought them, Parent #2 can use their Yubikey to save the day until a new one is purchased.
Yubico's USB A format factor "Security Key 2" is robust, but relatively expensive for what you need.
Searches for "Security Key" on Amazon or your preferred site will give you a pile of products and review feedback across price brackets, the only thing your parents are likely to care about are the connector (USB A is no use for a USB C MacBook for example) and maybe other form factor concerns like can it hang from a keychain, or would it fit in a wallet? For their purpose these things don't fill up, and shouldn't (modulo physically smashing it) wear out.
You can always buy a USB-A-to-USB-C adapter/converter. They are available everywhere, inexpensive, and if you're afraid it will be misplaced, there's always the option to glue the USB A key to the adapter...
Others have mentioned a desktop app, but how often do your parents have to 2fa? It's not every time they log in (unless they're buying a new burner laptop every time they log in. If they are, there may be other issues to discuss first.)
If you would like your parents to have better security for these accounts, I commend Security Keys. Unless your parents aren't together any more, or are just really fervently independent, it's probably fine to buy them one each, but with the suggestion that they both enroll both keys. This way when Parent #1 loses the Yubikey you bought them, Parent #2 can use their Yubikey to save the day until a new one is purchased.
Yubico's USB A format factor "Security Key 2" is robust, but relatively expensive for what you need.
Searches for "Security Key" on Amazon or your preferred site will give you a pile of products and review feedback across price brackets, the only thing your parents are likely to care about are the connector (USB A is no use for a USB C MacBook for example) and maybe other form factor concerns like can it hang from a keychain, or would it fit in a wallet? For their purpose these things don't fill up, and shouldn't (modulo physically smashing it) wear out.