It's extremely confusing, but Apple has two types of multple-factor authentication solutions in use.

The 'legacy' (my phrasing, only because it was the first implemented) MFA is SMS-based, and thus has not dependency on iPhones.

There's a newer (about a year or two old by this point) solution which has a 'richer user experience' and depends on having other Macs or iPhones to receive the MFA authentication dialogs.

The newer solution ("Two-factor authentication") also allows non-Apple phones to receive a code on their "trusted phone number". From the support page linked in a nearby comment:

What if I don’t have access to a trusted device or didn't receive a verification code?

If you're signing in and don’t have a trusted device handy that can display verification codes, you can have a code sent to your trusted phone number via text or a phone call instead. Click Didn't Get a Code on the sign in screen and choose to send a code to your trusted phone number. You can also get a code directly from Settings on a trusted device.

I believe Apple prefers that people use a trusted device as from their point of view this is more secure as they can verify the entire communications loop so they view this as a fallback option, but you certainly can use non-Apple devices to authenticate. They also don't appear to throw up any roadblocks to doing so.

Isn't the fallback only SMS/phone? That seems like a roadblock compared to say Google Authenticator.