I noticed on SERPs that some of the websites have a little gray arrow and when you click on it you get more information about this website. Some results don't have it. I attached a picture with an example. And I don't know what exactly it is and how to add it if possible.
Extended information
Just because you see extended information on the right side doesn't necessary mean they are using rich snippets. Popular sites are often favored and will return additional information obtained from other websites, for example in the Macy's it has a reference to Wikipedia of which is not something a rich snippet has done.
Off page signals
Google uses many off page associations from social media to information sites like Wikipedia to build up a richer search without doing anything other than have good standing with Google and plenty of visitors to make it worth while.