I'm sorry to say your bag of chips is lying to you. Isn't it amazing, that someone would lie to you to sell fried potatoes?
This isn't to say that the Inca weren't choosy about their agriculture. However, I've never heard of purple potatoes being particularly favored by the Inca. There are more than 4000 varieties of potato in Peru today - it was one of the earliest domesticates in South America and in every way is a staple to the diet. There is no particular preference toward purple potatoes today, except in the geographic sense (i.e. these potato varieties were grown in this valley by my grandpa, and his grandpa, and so on). But this only partially gets to your question because it involves modern treatment of potatoes. What did the Inca think of them? They would undoubtedly consider them to be important - left out to dry in the highland Andean sun, and mashed into patties, potatoes keep for months in storehouses and can act as insulation against famine. Combined with ch'arki (llama jerky also prepared through desiccation), the Inca moved armies rapidly through the empire, and fed teams of mit'a laborers (working to pay their taxes as was customary in the Inca empire).
These mit'a laborers often did work on lands that your potato chip bag is obliquely referencing: Lands of the State and Sun, special agricultural estates that were placed across the empire to grow specific crops. These included coca leaves (useful for ceremony and for motivating soldiers and laborers to work through the mild alkaloid buzz one gets from chewing them), aji peppers (a spicy and colorful kick, but the peppers can be choosy about where they grow), high-grade cotton for the production of fine Inca textiles, and of course the real love of the Inca, corn. Corn can be fermented into the beer known as chicha, which has low alcohol content but acted as part of the suite of rituals and ceremonies that bound Inca imperial affairs together - drinking chicha out of specially designed aribalo jars (often from Cusco) was a sign of acceptance into Inca suzerainty and the accompanying prestige. The lands of State and the lands of Sun were kept adjacent but separate - the State meaning administrative functions, and the Sun implying use for the cult of Inti and the various deities of the Andes. The empire also had special herds of llamas and alpacas maintained at high altitude for similar purposes (sacrifice, divination, fine textiles, and portage for military movement).
So while many crops were specifically selected for their use in ceremonies, the potato more than any other may have been the one crop the Inca took for granted.
I do apologize for the brevity of this response - I am out in the field (outside Lima) and can expand/update as people come up with follow-up questions (if there are any). It may be a few hours before I respond but it's not often we get questions about South America! I also recognize I don't have many sources, I will chase some more down when I have more time this evening. In the meantime, D'Altroy's The Incas is always a good start, and the work of Christine Hastorf on feasting and Inca imperial strategy is also fascinating.
You may want to post this over at /r/AskFoodHistorians
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