If you use SeaMonkey, clicking on the download link will work fine. As already said, SeaMonkey integrates a browser and an email client, hence you can install directly from the browser any XPI plug-in for the email client or for the browser itself. Just confirm that you want to install the plug-in when you're asked to.
You will then need to restart SeaMonkey. Once SeaMonkey has restarted, Enigmail will be ready to go.