You’re on the right track, the screencast helps. Yes, you only need to add the slideshow name, the slug will be generated from the name.
For the slides, you can upload multiple slide images at once like you did with the media uploader. But each slide must be added separately as a slide post using Slides -> Add New.
So when you are click the Use as featured image link in the gallery or media uploader, each time you click it you are replacing the slide’s image, not adding another one.
You have to go to Slides -> Add New, give it a title, click Set featured image, upload an image or choose an image, click Use as featured image, then close the media uploader, publish or save the slide and then go to Slides -> Add New to add another slide.
So although you can mass upload the slide images, each slide must be created separately, does that make sense?
This method works well for small slideshows like where the slides are used as banners to highlight certain areas of your site, but it could be cumbersome when adding lots of photos, such as a photo gallery.
It looks like you have not set a height or width for your slideshow. You should set these on your settings page. This will enable WordPress to automatically size the slide image correctly for you and size the slideshow so that the nav lays out better on the page.