I totally understand your position on this. You are the parents, you should give the best gift.
But if I were really struggling with money, I'd take the easiest way out. In ten years, your son won't care or won't remember that his AUNT got him a cool bike and his parents got him a lame video game.
If you hadn't taken the money, I might have had a different answer, but it'll make for some uncomfortableness with your SIL if you say "um no we're going to get the bike for him. Here's your money back."
Just my opinion. Obviously as parents we want to be the reason behind the big grin on our children's faces, but your SIL was trying to help and you took it. I think it's too late to go back on it. Please post a "So what happened" in a week or whenever something happens. I'd be curious as wo what ended up happening on this one. It's a tricky situation.