First, remember that like all homebrew, DOOM needs custom firmware to
be installed before you can run it. If you're on official Sony
firmware, you'll need to install 3.71 M33-3 from Dark_AleX. You can
find guides on doing so on most PSP forums, like MaxConsole, QJ.net,
and exophase.
Assuming you do have custom firmware, simply un-zip the Doom folder
from the zip file into the GAME or GAME371 folder of your Slim. All
the files in the Doom folder are required for Doom to run. Simply
copying the EBOOT.PBP will fail. Note, you don't need to do anything
with the src folder in the zip. That's just for developers and people
interested in the source code to Doom.