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.

Something like this is really going to be a challenge for them. Might be time to move them to fastmail.

> USB A is no use for a USB C MacBook for example

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...

Google discontinued the "read you a number over a landline" feature a little while back and only supports texting now.

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.)

I've found Google asks for 2fa at pretty random times. I do travel a lot but still it happens at least once a month.

I am curious about this as well parents in the same position. What happens now?

My Dad is in the same boat. What about a Titan/yubikey? They are fairly easy to use - although you might have to help your parents with enrollement.

low tech, but with google account?

Yeah they can barely manage email. I've taught them how to forward email a dozen times but that's a bridge too far for them.