I’m not aware of any out-of-the-box solution (I’ve just started to play with Hugo), but depending on your experience, checking the source code of the plugin you’ve mentioned might be useful - it’s opensource, I’ve found the (SVN) repo of it here: https://plugins.svn.wordpress.org/wp-appbox/
I tried to figure out how it works but it is more complicated than how it looks like.
I wrote to the developer asking for information though, waiting for an answer.
I didn’t find anything of similar in JS either - but I’m not sure if I was correct since english is not my mothetongue and I was difficult to me to give it a name different than “app box”, “android label” “android badge static sites” etc.
I ended up creating manually a responsive div box and inserting manually icon, title and url of the app as a simple shortcode.
JQuery didn’t help me to retry the information right from Google Play, furthermore I couldn’t install any node.js library to help me doing so, so I opted to a simple a manual solution.