The only thing missing from that tutorial is adding the layers to the composition. Your screenshots do not show the position property of any layers. Select all layers, press "uu" to reveal all modified properties.

If you do not see position keyframes you have failed to copy, then paste the path data. My workflow is just slightly different than the workflow in the tutorial. After I have drawn the path on a layer that has not been moved, rotated, or scaled I set one keyframe by pressing Alt/Option + m. Then I immediately Cut that keyframe using the keyboard shortcut Ctrl/Cmnd + x. This assures me that I have copied the path data to the clipboard.

Then I select the layer that I want to animate and press Alt/Option + p to set a keyframe and immediately use the keyboard shortcut Ctrl/Cmnd + v to paste the vector path data to the position data. Setting and cutting or copying keyframes guarantees that you are going to copy the keyframe data. Just selecting Mask will not. You have to actually have the path selected. Using the keyboard shortcuts minimizes moving around the mouse and keeps me from accidentally grabbing the wrong property or just a portion of the path. 

Let us know if you have any other problems.

Check out this Adobe tutorial that can help you.

Animate an object to follow along a path

What tutorial are you following? Most of the ones you find on YouTube are not much more than recipes that an enthusiast has copied and many of them have poorly explained and often pretty inefficient workflows. 

If you are brand new I suggest that you open up the Learn Workspace or the Learn Resources on the Home screen. You should also spend some time with the User Guide. It is available on the landing page of this forum and the AE Product page. You'll be a lot better off a lot sooner if you start with some good training materials and then move on to creating something original.

You forgot to upload a screen capture of your composition.