You need to have a free dropbox account. (dropbox.com) Once you have one and have set it up on your computer, (and on desktoppr.co, just go to settings to link it) you click the little cloud button next to the image and it will be synced to your dropbox account. Simple as that.
That should be mentioned during the setup of your account. It says it's optional and can be added later. I assumed you could still browse the site and manually get to wallpapers if you didn't want them to go to your dropbox.
Yeah, that bothered me too when I first did it. I didn't have a Dropbox account so I skipped. Once I figured it out, I made one, (it's free!) and there ARE some benefits to having one as opposed to just downloading, but I agree. There should be a way to regularly download. But, it IS a beta, and perhaps they don't have the server space yet to host all those pictures. So, for now, Dropbox is the best solution.