There are lots of different ways to do any one task in Photoshop. Here is what I think might be the most straightforward method with how you have your image set up. Before we start, it can help to go to Edit > Tools... and make sure Show Tooltips are turned on.
With your layers as they were at the end of your video...
1. In the Layer panel, click on the layer with the shape you combined that you want to select inside and make transparent (I believe it was labeled "Inside")
2. Select the Quick Selection Tool (keyboard shortcut W)
3. Drag inside the shape. The Quick Selection Tool will make a selection of the area up to the edge of the black outline (the area you want to be transparent)
4. Select the gray shape layer in the Layer panel (I think it's the layer labeled "Outside")
5. Go to the bottom of the Layer panel and click the 3rd icon from the left to create a layer mask (When a layer mask is applied to a layer, anywhere there is black the pixels in the layer won't show up, and anywhere it's white the pixels will show up. Levels of gray in the mask will affect the opacity of the image).
6. We're close but not there yet. The layer mask is masking the opposite of what we want (the outside portion is hidden and the inside is still showing). To swap the black and white, make sure the layer mask is still selected and go to Image > Adjustments > Invert.
The gray shape should now be transparent inside of the area outlined in black.
Let me know if you get stuck or need help understanding any of the terms I used or any of the steps.