Edit: See below.
I've got the same problem. I can't sign in to my dev. account from my Windows 10 computer running Chrome. I do that often to check Sales and Trends to see how my apps are selling. There does not appear to be a way to do that anymore. I guess whenever I want to check anything about my account I have to boot up my Mac. I do mostly Windows development and I don't really use the Mac unless I am developing an update to one of my apps. This roll-out of two-step authentication was not thought through very well.
Edit: Here's what worked for me. I booted up my Mac and tried to sign in to my dev. account using Safari. Initially I got the same message. But then I followed the directions for enabling 2-factor authentication on my Mac, which involves going to System Preferences / iCloud. I had never signed up with iCloud before , but I did it now and it was easy. Then you go to Account Details and select Security tab. If two-factor authentication has never been turned on for your account, there will be a button for "Update Security" which will guide you through turning it on. Once it is turned on, leave the Mac running and try to sign in on another non-Apple device. It will send a notification to the Mac and a verification code will pop up on the Mac screen. This verification code can be entered on the non-Apple device and then that device will be authorized to access your dev account.
I still think they should have streamlined the instructions to make this clearer as to exactly what you have to do.