We're still skirting the edge of the real problem here. Of course in Inca had fat - no human civilisation can survive without it. Animal fats can be rendered from almost any species (very efficiently from many marine mammals and birds, with the penguin being named for the fact). Thousands of plants make more or less effective oilseeds.
To get the oil to the required temperature is a different issue. You can do it by heating a pottery vessel *in* hot coals. Eventually (if you're nuts enough) this can be brought to red heat. Regulating it is tricky. Unglazed porttery, even of the highest quality, has a way of lettting liquids seep in, and you hae to deal with occasional flameouts from fat diffusing through the walls. Deep-frying in pottery of any kind is a risky proposition because if the vesels splits (as pottery will, sooner or later, no matter how good you are) you're nmot just looking at a loss of some perfectly good food, but also a major fire hazard. Glazed or unglazed earthenware only makes a marginal difference. Real porcelain or hot-fired stoneware are much better. But the thing that makes deep-frying an easy and relatively risk-free technique is a metal vessel - 100% fatproof, high heat conductivity, not prone to bursting or serious overheating and able to work with even a relatively small fire.
I'm not sure gold is the ticket.
So while it is possible for Pre-Columbian Andean civilisations to invent chips, making them would be the preserve of seriously skilled cooks and probably very wasteful of fuel and time. Given the narrow margin of survival that characterised most of them, it would be the quintessential luxury food.