I think it's safe to say that something like this has not been used as the core part of any other popular card game out there. At least, none that I've heard of so far.
In Arrows, rotating and/or moving cards around on the field are two of the most powerful things you can possibly do in this game.
In the above image, your Field card is getting a boost from one of your Arrow pieces (which boosts red numbers), so it's able to attack with a lot of power. What, if, all of a sudden, the opponent used a card that is used to swap the positions of two enemy cards? And after swapping the current two cards...
Your Field card can't attack anymore since it's in the back row. Not only that, but your Arrow Piece is now stuck in the front row leaving an open spot for enemy attacks to pass straight through. Simple movement like that can really change the flow of the game.
Rotation can get even more interesting. All of the cards are purposely shaped more square-ish for the purpose of possibly being rotated later. This doesn't apply to Field cards as much as it does to Effect cards, though. Consider this:
The cards with the blue and red circles on them are enemy Effect cards that increase attack power to the Field cards they point at. The plus signs show what cards are receiving these boosts.
Imagine that you had two different Special cards (I'll cover them in the next part; for now, to keep it simple, think of them as instant-use things). One of them destroys all enemy Effect cards on the field; the other one rotates them all 90 degrees in any direction. Which card would be better to use? In this case, rotation is actually more powerful then destroying the cards, especially if it's used like this.
Can you see what happened here? The enemy Effect card in the corner has basically been made useless, and the other one is now actually powering up your own Field card! Also, there isn't an easy way for your opponent to simply take their Effect cards off the field, so it also leaves openings that they can't defend with Field cards.
There are some Field cards that have attacks in all 8 directions. Only the 3 that point towards the enemy matter at all, but each time your turn starts, the card automatically rotates 90 degrees. Simply put, it means that the card's attack power changes every single turn. Taking advantage of what way the cards are pointing is a huge factor in winning.