This game doesn't seem very safe... throwing plastic birds around trying to knock things over? But the kids are incessantly asking for it.
It's actually not nearly as unsafe as it seems. For one thing the birds are soft rubber squeeze toys. I've been hit in the head with them and it barely stings. The catapult for launching them is pretty weak, at full pull you can fling them about 5' distance, and about 3' in the air.
To be honest, if your kids are asking for this game by name, they're likely already familiar with the concept of the game and are trying to implement it with their existing toys. I'd much rather sit down at the table with my family and this game than walk into my son's room and find him throwing stuffed animals across the room into piles of blocks or lego castles. (Been there, done that.) Now that he knows we have the game he asks to play it instead of staging it with his other toys.
Just because they want it doesn't mean they need it and doesn't mean you must get it for them. It sounds to me like you don't want to get it for them but you also don't want to disappoint them. This is a great time to teach them that want and need are two different things. Teaching them that they don't always get what they want is a good lesson in growing up. As well, it does seem dangerous, even if it doesn't hurt what are you teaching them about throwing things in the house, which can break things even if they don't hurt people. As well, why do they need to be throwing things in the house? Teaching them that there are rules and there are inappropriate items out there that they just can't have is an important lesson (as I stated above, but it deserves repeating). Stay strong to what you think is the right thing to do, sound like not buying it, and remember that you are the parent and know what is best.
All in all I recommend not buying it and if they complain teach them that sometimes we don't get what we want. That everything they need and most things they want they get, but sometimes the answer is no.