Customers are weird these days

Question

It's been a slow day at The Board Game Store™ when the familiar ring of a bell brings you back from your daydreaming, alerting you to the presence of a customer. You look over and notice the oddest customer you think you've ever had. They're wearing fuzzy bunny slippers, a majestic horse shirt, a long necklace with some kind of red fish, and what appears to be an elephant hat with huge ears and a long trunk.

Not wanting to be rude, you begin talking with the newcomer. "Hello! Is there anything I can help you find?". The customer walks up to the counter and smiles.

I'm looking for a board game for 2 to play.
The key is the rabbits, or so they say.

The board is a grid, similar to the checker.
Beware the traps, though, unless you have a protector.

There's natural enemies, like the cats and the dogs.
Some frozen in fear, like a petrified log.

You respond, "You speak as if you're the Cat in the Hat! Pardon me please, I must look in the back." As you scour the shelves, you don't find the game they want. You grab the alternative and bring it back to the front. "I could not find the game you requested. We have plenty of these, though, and it can work as a perfect substitute."

The customer agrees to accept your suggestion, agreeing that it will work perfectly, and says they'll be back later to pick up the official game.

What did you give them and what are you going to order?

Answer 1

This is the board game

Arimaa

Which is played with

Rabbits (slippers), Cats(Cat in the Hat), Dogs, Horses(shirt), Camels, and Elephants(hat). Unfortunately, it lacks Red Herrings (necklace), but that's probably because it's played on land.

I'm looking for a board game for 2 to play.
The key is the rabbits, or so they say.

2 players, and You win by getting a rabbit to the opponent's home row, or by killing all of your opponent's rabbits.

The board is a grid, similar to the checker.
Beware the traps, though, unless you have a protector.

Played on a 8x8 board, you lose pieces by having them on "Trap" squares without a neighboring ally.

There's natural enemies, like the cats and the dogs.

Cats and Dogs are among 6 piece types each player has

Some frozen in fear, like a petrified log.

Animals are frozen if they have a stronger Enemy neighbor, and no Allied neighbor.

You gave them

A Chess set, which has the same board (mostly, traps missing from C3, C6, F3, and F6) and pieces in the same distribution.