Here are the differences between my viewport and the Tutorial's viewport. Q. How to show the small orange cube and the object data?
The 3 axes arrows has become the orange cube, and the pen icon has become the green squiggly line.
The icons have been changed since the tutorial was recorded in the early stages of the Version 2.80 and the icons were not final at the time. But you should find the same information in these submenus.
Although I think there has been changes to how the grease pencil object data works so you might see things arranged differently.