In order for the game to know how to connect you, it has to share "cookies" that track who you are with Amazon Web Services, who provides the web browser service.
The following instructions will fix this for Chrome, although the principles will also apply to other browsers.
In Chrome, enter the following in your URL bar to get to the right settings page: chrome://settings/cookies
From there, you will likely see that you are blocking third-party cookies. If you don't care about this, you can turn that on to "Allow all cookies" and that should resolve the problem.
There, enter: [*.]aws.amazon.com and click to confirm. This allows a variety of URLs from AWS services at Amazon (but not Amazon the store) to install cookies.
That's it! From there, you should be able to go back and try to play the game in the web browser again. Let us know if this does not work for you using the blue chat on this site.