I believe, though I'm not certain, that the bit pictured has a piece of metal cable through the middle for safety, so the horse can't just bite the bit in half, there is still SOMETHING in there holding it together. I wouldn't want to use one of those bits because what if the horse chews down to the cable while you are riding and then it cuts the mouth without you knowing the bit was damaged.
I can't say about this one, but I own a rubber bit, and going on the way it flexes, it doesn't feel like there is anything other than rubber in it. I kind of like having it around, so I won't cut it in half just to find out.

They are usually considered training bits, and it is my understanding that some types of competitions specifically exclude rubber bits (most likely as a safety issue).