Hmmm. I don't know if can tell you anything much different than what the instructions say that are printed on the template, but here are some tips I hope will help:
1)Very carefully examine the numbers on the template. Matching numbers should be glued together. 2)First, glue together the parts that are on the second page of the template. 3)Second, assemble the "interior of the chest" and glue it to the "chest rim" as indicated by the matching numbers. Then glue the "interior of the chest" and "chest rim" assembly inside the bottom of what you built in step 2. 4)Third, glue the lid interior inside the top part of what you built in step 2. 5)Then you are done!
Now I am the one who is confused. If I understand your question correctly... Yes, the images of the parts you see in the template are the ones you are supposed to use to make it. As it says in the instructions on the template, the two pages of parts need to both be printed out on card stock and then the pieces cut out with an exacto knife so that they may be glued together. The words you see that say "cut out this piece" are referring to the white part in the middle of that one particular piece (i.e. there needs to be a hole in the middle of that piece.) Did I answer your question?