Gateway uses propriety motherboards in most of their models, which don't fit in standard cases (not all, but most will not). Pretty sure yours is one of these that will not fit a standard case.
The motherboard does have one pice-e x16 slot, so you can fit a a small video card in there. I would recommend a low power card, like a 6670 or a 7750. Now I think the standard cards will squish in, if not look for low profile models.