CTRL-click

Open the template

Delete everything in the layers panel except the groups titled

iPhone > 120 Retina Home Screen
Rounded Mask

Delete every layer except the two layers highlighted here:

Command/CTRL-click the mask thumbnail on the "Rounded Mask" group. This will load the mask as a selection (you'll see the marching ants)
Grab the Marquee Tool, hold down the Option/Alt key and drag selections over the areas which are not the 120ox icon. So that, in the end, you are left with marching ants only around the 120px icon.
click the "120 Retina Home Screen" group in the Layers Panel to highlight it.
Click the New Mask button at the bottom of the Layers Panel. Things should look like this:

Drag the "120 Retina Home screen" group out of the "Rounded Mask" group. (So it's not nested inside the "Rounded Mask" group).
Drag the "Rounded Mask" group to the trash icon at the bottom of the Layers Panel.
Choose Image > Trim from the menu.
Tick Transparent Pixels in the dialog box and click OK.
Expand the "120 Retinal Home Screen" group in the Layers Panel and edit the "Artwork" smart object layer with your art. Or simply add a new layer containing your artwork.
When finished, choose File > Save For Web to save your image for the web. (Do not use any of the actions associated with the template.)

Essentially all you need is a 120x120px document with a rounded corner mask. That can be created a number of ways, many of which are faster and less convoluted. Based upon your initial decision to use this template for something relatively straightforward, I think the above explanation may be the most beneficial to you.

Same thing in 5 simple steps.....

New 120x120px document
Draw a rounded rectangle using the Rounded Rectangle tool (it doesn't matter what color the rounded rectangle is.
Place your artwork as a Smart Object layer above the rounded rectangle layer
Hold the Option/Alt key down and click the line, in the Layers Panel, right between the art and the rectangle layers.
This created a Clipping Layer which restricts your artwork to only within the rounded rectangle. This adds the rounded corners to your artwork.
Choose File > Save for Web... to save the image.

To be frank, this is very simple Photoshop stuff. There shouldn't be a need for a "template" or anything pre-constructed. All it takes is a basic understanding of tools and the Layers Panel.