All screenshots are taken by running elisp/emacsThemes.el. If you want to add a screenshot, you can edit emacsThemes.el and create a pull request or open a new issue for this repository and I'll add it myself.
The "popular" sort order is based on downloads from MELPA, a statistic that is retrieved every time you visit the themes gallery website. The themes that lack a download stat are themes that are bundled with emacs.