Hi Mike,
Since no-one who knows more than I do has replied, I will just confirm that the same thing happens to me. Mahab posted on 26 November seeking help with a similar issue - also no reply.
I can only assume that the GE plugin does not support IE 11, at least not on a Windows 7 platform, anyway. The GE plugin seems to regard it as an unsupported browser type. It worked just fine with IE 10 for me too.
Despite my searching, I cannot find any 'official' word from Google on this issue. Maybe it will be fixed in a subsequent release of GE, who knows? Disabling Enhanced Protected Mode in IE 11 makes no difference - in any case, all Google sites are rendered in a 32 bit process for me even when using Enhanced Protected Mode.
Cheers!