I've been keeping out of this up to now because I must say I don't really get what the big joke is either, and I have no idea where this "Inside this [place name] shirt is one terrific kid" thing comes from, but....
1. There's no problem with the omission of 'there'.
2. A T-shirt is a kind of shirt and can therefore be referred to as a shirt in the appropriate context.
3. If it just said "Terrific Kid" on it, that would be boring. That it says "Inside this shirt is a ..." makes it ever so slightly amusing, as it sounds like something one might read on product packaging. However...
4. For me it does not conjure up the image of the kid being wrapped in the shirt.
5. Pulling a T-shirt up over one's head and running round making monster noises seems to be something some children do. (Even as a child I just found this stupid and annoying.)
6. Terrific doesn't normally mean furchterregend. I would translate the slogan as In diesem T-shirt steckt ein grossartiges Kind. Maybe the joke is that this is the normal meaning, but by pulling the thing over its head, the kid inside can exploit the (weak) pun and turn itself into ein furchterregendes Kind.