Ah, I see. This needs a bit of an explanation then.
As you can tell, the thumbnail feature is still a work in progress and a lot has changed from the version you’re currently using (2.1.4, correct?) to the most recent releases of the WordPress Popular Posts plugin.
Back then, WPP relied on Timthumb (a third-party PHP script) to generate thumbnails. However it seemed to cause more trouble than benefits so in later versions of the plugin I decided to switch to the Feature Image since it’s a core WordPress functionality and works out-of-the-box. No extra configurations needed, no need to play with file/directory permissions. The drawback was that people had to set their own images manually for the thumbnail to work. That turned out to be a major PITA since, well, basically everyone was being forced to set a thumbnail for each post – nobody liked it, as expected.
Because of that, on a more recent version (2.3.0 or earlier, I believe) I re-added the possibility to have WPP pick the images for you – only that it has been relocated to wp-admin > WordPress Popular Posts > Tools. By default, the plugin is set to get the thumbnails from the Featured Image (hence why most of your posts are not displaying a thumbnail) but you can change that to First image on post and the behavior will be the same as on 2.1.4.
Hope that helps!