Go to the menu bar on the top of the screen, click and hold the left mouse button, move down to quit, then release the mouse button.
What is happening here? Double clicking on "About HyperCard" opens a document in HyperCard. What you were calling a dialog box is actually a window containing the document. The "close box" in the top right hand corner is actually a resize button. It doesn't appear to resize anything since the Macintosh tries to make the size of the window fit the size of the window contents. Since the contents already fit, it did not have anything to do. For whatever reason, they decided not to include a close button. A close button would have been a single square in the top left hand corner. I don't know why they omitted the close button, but I am guessing it is because of another peculiar behaviour of the Macintosh: closing a window does not quit an application or even return to the desktop. Normal behaviour simply left the application menu on the top of the screen, with an apparently empty desktop. (For those who have used old Macs, I'm referring to the era before Multi-Finder.) This would have been confusing in school environments, particularly with really old versions of the operating system.
If you think those behaviours are mind-boggling, I would suggest trying out RISC OS. GUIs of that era behaved differently from each other since standard behaviours had not been established yet.
EDIT: trying to make the description more clear for someone who has not used Macs prior to System 7.