Hi there,
I think the only way to do it without a plugin is to handpick the popular posts then build that widget manually by inserting pictures and titles.
Something like this would be best handled by a plugin as there needs to be some sort of logic that determines what a popular post is.
Here are some suggestions:
https://www.wpbeginner.com/plugins/5-best-popular-posts-plugins-for-wordpress/
I couldn’t tell which plugin the example is using unfortunately.