No input fields for the Apple ID Verification for the iMac 10.10.5
Got exactly the same problem today, e.g:

have two-factor auth.
tried login to icloud on some old macbook (OSX Lion - 10.7)
on my iphone i got the code
but on the macbook there are no input fields - e.g. impossible to enter the code - there is no place where.

More googling and I found this page: https://support.apple.com/en-us/HT204915 where says:

What if I use two-factor authentication on a device running older
software?
If you use two-factor authentication with devices running
older OS versions—like an Apple TV (2nd or 3rd generation)—you might
be asked to add your six-digit verification code to the end of your
password when signing in. Get your verification code from a trusted
device running iOS 9 and later or OS X El Capitan and later, or have
it sent to your trusted phone number. Then type your password followed
by the six-digit verification code directly into the password field.

So, in short: if you didn't get the input fields, do the following:

on the trusted device &quot;Get the verification code&quot; how - see this
and on the device without input fields enter your password, immediatelly followed by the 6 digit code - e.g. &quot;MyPassord123456&quot;

That's all - it works. :)