The intention behind the plugin is to move commenting from WordPress to Discourse. Discourse offers a lot of moderation and community building features that don’t exist in Disqus. It would not be possible to keep these features if comments were added directly below the WordPress posts.
If you plan to keep using Discourse for comments, you will need to add some CSS to your theme to correctly position the comments on the page. Discourse comments are currently being displayed at the full width of the page. All the other content on the page has it’s width constrained by a container.
One thing I noticed on your site is that the Discourse System user is being included in the participants list. I think the Discourse WordPress plugin should be updated to remove the System user from the participants list.
If you would like posts that are published from WordPress to Discourse to be published under your username, instead of by the system user, go to your WordPress profile page and enter your Discourse username into the Discourse Username field of the ‘Contact Info’ section. In the next update to the plugin, the Discourse Username field is going to be moved out of the ‘Contact Info’ section and into a separate ‘Discourse’ section on the user profile page.