These settings seem to be stored in the file:
~/.zotero/zotero/_your_profile_name_here_/zotero/locate/engines.json
I was able to restore the entry by picking a copy of this file, e.g. from GitHub:
wget -O ~/.zotero/zotero/_your_profile_name_here_/zotero/locate/engines.json https://raw.github.com/robinpaulson/impero/master/engines.json
Note: I assume a *nix-systems, but I guess it should work similarly on Windows-systems.