Using product key worked
I also got this message. Tried to sign in via Excel, Word, Powerpoint, all with same result.
Then went onto the My account page at office.com/myaccount. This acknowledged that I had purchased the product and the date I had installed it.
Then I noticed under the "Get Started" section there is a link to reveal my product key -this is not the same number (although starts with same letters in my case) as the number on the scratch panel of the card that I got when I purchased the product in a shop.
Then I returned to Word, selected Activate, got the sign in dialog box, and this time instead of inserting my username and password I chose activate via product key instead. Copied the key from the office.com/myaccount page, pasted it into the field, and it worked!
Summary: get product key from office.com/myaccount, use that instead of user name and password to activate the product.