It's because on that example the results window is placed on a different location with the results shortcode. Also, the layout position of the search results is set to “blocking” and not “hovering” – meaning that it's not hovering above the surrounding content, but rather pushing it down.
Here is a link to a guide on how that example was created: https://wp-dreams.com/knowledge-base/two-column-search-setup/
There is also a brief explanation on this in the documentation: http://wp-dreams.com/demo/wp-ajax-search-pro3/docs/#positioning_the_results_elswhere
The “hovering” result list is resized to the search width because of the absolute positioning. The “blocking” results list however has auto width, so it will be as wide as the container element.Best,
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