You're missing the part at 2:30 in the video, where he adds a Layer Mask (not a Vector Mask, as he calls it). You then make sure the mask for the layer is selected, and do you work on that. You will see this is the Channels panel.
Your mistake: You applied the gradient to the layer 1 image.
In the video at 2:35 you can see that the layer 1 gets a layer mask first - your's haven't got one.
Then apply the gradient to the layer mask, not to the image.
Both the above answers are correct , perhaps this will help explain.
When a mask is attached to a layer, where the mask is white - the layer shows. Where the mask is black - the layer(s) below show. Shades of grey result in degrees of transparency.
In the example below the red and green layers are both solid but a gradient was applied to the mask by clicking on the mask in the layers panel then using the gradient tool.
I hope that helps