I agree, I like the concept of scaring. I think a scared piece should remain scared (immobilized) until the ghoul is captured, or the ghoul moves, or the scared piece is captured. Then you can look at the board, and know that all pieces within the attack range of a ghoul are immobilized (no need to keep track of whether each of the four ghouls has just moved).
This make the ghoul pretty scary, even if it just moves 2 squares in any direction. A ghoul scares, then on the next turn can capture the scared piece. Almost the only defense is to apply a counter-attack, so that a ghoul that captures is captured in return.
What happens to a king that is scared? The king would be both scared and in check. The king can't get out of check because he is paralyzed with fright. So a ghoul can checkmate by himself!

A perfect ending for a game with ghouls!!

This is a very subtle thing, but I think "scaring one piece" needs to be refined a little before it is put into use.
Chess is game of "perfect information" and it's also (almost) a game where everything can be known by looking at the board. By perfect information, that means that both players have all the information about the game. (Unlike games where some information is secret, or games of chance, like poker which has both chance and secret information).
If there is a piece that scares one piece, then you have to inform the opponent which piece is scared (like the bishop or rook in example above). Technically this is still a game of perfect information, but you can't tell which piece is scared by just looking at the board. For a real board, you can either show the scared piece by putting a chip under it, or in a diagram you can circle the piece.
Maybe a ghoul which scares "All pieces" in its attack range. This would obviously make it more powerful. The only defense would be to block the attack - but then then the new piece also gets scared. Or the opponent could start a counter-attack (get attention away from the first attack). Or the opponent could just plan to lose the scared piece, but make a plan to capture the attacking ghoul.
This "new" type of ghoul could create new and interesting strategy. So now we have a bunch of ideas, and two names since I accidently said "ghoul" instead of "zombie". Things to resolve:
1) What's the name, zombie or ghoul?
2) Does it move in orthogonal directions like a rook 2 squares, or in all directions like a king but 2 squares?
3) Does it scare just one piece (Arjun's idea), or all pieces (my idea)?
4) Last: who's the first to play with this new piece? I can't take a new game right now, but maybe later I'll try.