The Tibetan Mastiff can take high altitude better than generic dogs, or so breedists would like you to think. Some of the genetics changes are similar to those seen in human Tibetans – regulatory changes in EPAS1, for example. Domesticated dogs haven’t lived in Tibet all that long – but wolves have. The Tibetan Mastiff picked up some of those useful variants from local wolves, even though the amount of admixture wasn’t large. Adaptive introgression, just as Tibetans seem to have acquired their high-altitude version of EPAS1 from Denisovans.
Andean Indians didn’t have any archaic humans around to steal adaptations from. They have had to develop their own altitude adaptations (in a relatively short time), and they aren’t as effective as the Tibetan adaptations.
Naturally you are now worrying about sad Inca puppies – did they suffer from hypoxia? There are canids in South America, like the maned wolf and the bush dog, but they are probably too divergent to be able to hybridize with dogs. The chromosomes are different, so pre-Columbian dogs probably couldn’t acquire their alleles. Moreover, the dogs of the Amerindians seem to have done poorly in competition with Eurasian dogs: I know of only a few breeds [the Carolina Dog, for example] that are known to have significant pre-Columbian ancestry. Perhaps Amerindian dogs were also scythed down by Eurasian diseases.