Interesting, when you parented the rifle to the armature did you choose Armature Deform With Empty Groups? That’s what will create a group for each of the bones in the rig.
I’m using my own mesh and did it exactly like you show on video. When I add groups manually and assign to parts of my mesh, they don’t move it. Only root bone works.
Oh I see! It’s because the armature modifier takes one armature as an input while all of your bones are separate armatures. Quick fix is to select all your armatures, make the root the active object, and press Ctrl+J to join.
For more about working with armatures and bones, I would definitely recommend Wayne’s new rigging course: