Yes, the El Capitan installer file deletes itself when you install it by running the installer.
However, the name of the El Capitan installer app is "Install OS X El Capitan"
The Installer app appears in your Applications folder, after a successful download of the installer.
It automatically runs, again after a successful download.
And, after installing, it deletes itself.
The file that you have is too small to be the El Capitan installer (showing 5.66 GB).
The El Capitan installer will be about 6.08 GB.
The file that you see is likely just an incomplete download.
Either way, I think you can safely delete that file. I don't think it is anything that you can use anyway - not a complete download.
The full El Cap install app _normally_ is found in the Applications folder.
Not sure why the full app would stay in the App Store folder, which is, in effect, a temp folder for App Store downloads.
You could open your App Store, then check the Store menu for "Check for Unfinished Downloads". If anything shows up, that may properly complete that download. Then quit the App Store, and reopen it.
That may clear out that item without you manually deleting it.
But, if it stays through a restart, and a relaunch of the App Store, then certainly manually delete it.