Q: Two-Factor Authentication is not available for Child's Apple ID?

You'll need to enable two-step verification by logging into their ID at https://appleid.apple.com/

You can enable two-step verification with any Apple ID, not just those upgraded to iOS 9.3

Two Step requires both ends (web & device) to be on the same page.

I believe if you enable it on the web site it enables it on the devices. I never enabled mine on my device, only through the web site. I have kids in the Family Sharing and logging into their accounts online, I see the option to enable two-step verification.

In doing some more looking it looks like two-step verification and two-factor authentication are two different things.

I see the options to enable two-step verification from my kids' devices from the web site. I would need to check on their devices when I get home to see if two-factor authentication is there or not.

My son's account looks different when logging into https://appleid.apple.com/

I just tested by changing my son's birthday to make him younger than 13 and sure enough two-step verification was no longer listed as an option to enable.

Yes, they are 2 similar but different security methods.

Two factor is newer and in theory, easier as it does not rely on a key to remember/store. It's all based on trusted devices.

I think the terms you are quoting are for iCloud only, not Apple ID.