The RobotiQ Hand-E gripper in the RoboDK Library is set up as a robot instead of a tool. Not sure why aside from it being a mistake on export for the library. With it being labeled a robot and not a gripper it doesn't automatically attach to the flange like other tools do.
If you want to see the moving RobotiQ gripper mechanism you should place the RobotiQ mechanism attached to the robot.
On the other hand, if you want to use it for programming, you should add a tool (TCP) with or without a 3D geometry. This tool should be directly attached to the robot item. Tool geometries are static and can't be moved like mechanisms do.
Tools (.tool) are automatically mounted on the robot flange. Mechanisms (.robot) are not, you need to drag the mechanism manually under the robot to attach it.
However, it will not act as tool (it is for visualization). You can define a Tool with no 3D model at the right location (right-click robot, Add Tool).
Tool files do not currently support movements or Programming (like RobotiQ would require). For that reason we defined tools that require movement as mechanisms so users can get the functionality they would expect of a dynamic tool.
This is just a technicality because as my colleagues mentioned, it does not affect functionality and there is a proper way to use these tools.