What you're looking at is actually called the "expanded user card."
When a user fills out the About Me section of their profile, and the text within it is at least 6 characters long, the user card will expand.
The user you hovered over first in your .gif demonstration, Mad Scientist, has a blank about me at the moment (this text field becomes "Apparently, this user prefers to keep an air of mystery about them." when a user hasn't filled out their about me section.) As a result, their user card will not expand.
Test it yourself! Head on over to your profile's edit page, clear out your About Me section, save your changes, and then come back to this page. Then, hover over your avatar, and you'll notice that the card will not expand.