I actually hadn't opened TeamViewer in awhile (I guess that's a good thing, means I didn't have remote issues to support!) so I tried it. I had a similar issue, but I found I had to click on the "Sign In" button rather deliberately, twice...and then an extra dialog appeared like this one:
I had to check my email and add my device as a trusted device and then try the login again. (Again some deliberate clicks on the "Sign In" button!)
Maybe you need to do the same thing?