While I can't speak to the actual reason your game exported in a separate window, did you rename the .html file in the export to index.html? Other than that we more or less used the default settings for HTML5 export.
edit: Your game plays in the webpage window for me! Looks great!
And thank you for the kind words! Our goal going in was simply to have finished a project, and I personally am really happy with the results, hoping to take these lessons forward into the next jam!