2.80 (sub 45), 490a385c8124, 2019-03-02 00:57
Grease Pencil objects have more advanced display modes.
You have to go to Object Data tab (Pencil icon) ,not Object tab (Square icon) showed in the video.
This tab contains Strokes panel.
In this panel, change Object Depth Order setting from 3D Space to Front.
Maybe there could be a check to automatically switch Object Depth Order when option in Viewport Display panel is enabled.