Game chips are a vague concept. They are, at their most basic, potatoes that are deep fried and served hot, as a side dish to game (typically venison or game birds).
Things then become complicated, and more so if you are speaking to Americans. Game chips may be cut thin and deep fried as are crisps ("potato chips" in the USA), or cut into larger chunks, as are chips ("french fries"). However, in either case they are usually cut as rounds -- except that in ~20% of cases (by a google image search) they are actually cut as wedges or strips. The thicker rounds may also be waffle cut (AKA waffle chips, "waffle fries").
Also, they do not have to be made with potatoes. Carrots, beets, parsnips, and of course, sweet potatoes are also used. Additionally, they tend to be fancier than chips/crisps, with seasoning including rosemary, thyme, basil, black pepper, garlic, and/or onion powder in addition to the traditional salt.
In short, if you order game chips, you do not know what you will get. However, it will be a fried root of some sort, and will be served alongside a freshly killed animal. If this is not the case, send them back.