If I may step outside canon for a moment, "Mystics" sounds to me exactly like the kind of name a historical Western foreign culture would give to a non-Western foreign culture. (Indeed, in the retranslation the word used is "Demons," not "Mystics.") In this case, "Mystics" is almost exactly analogous to the old term "Orientals." "Orientals" was used primarily by Western peoples of Eastern peoples, and not by Eastern peoples to or of themselves, unless conversing with Westerners in a Western tongue. These sorts of names (whether appropriate or not) are ethnic in nature, and therefore by convention should be capitalized.
Lay names for species are not capitalized: humans, tabbies, carp, crows, etc. This would also be true of individual Mystics if we were to describe them by their unmentioned speciary names. But if we were to speak of a species taxonomically, certain capitalization rules come into play. Our species is called "Homo sapiens." You will notice the capitalization of "Homo" but not of "sapiens." This is because "Homo" is our genus and "sapiens" is our speciary qualifier, and, by convention, all the ranks in taxonomy except for that of species are capitalized. Species names are given as two-term names where the second, speciary word modifies the first, generic one, rather than standing alone. All species described by our rules of taxonomy are subject to the same grammatical conventions, including any hypothetical Mystic species, were they to be described taxonomically.
There is another convention at work, which is that of homeworld affiliation. In science fiction, a fellow sapient species is often characterized by its homestar name or its homeworld name, and these names are always capitalized. For instance, we humans are also "Terrans" and "Earthers" (or the somewhat more derogatory "Earthlings"), for our planet. I am not aware of any common name for humans as a function of our star, Sol, but whatever names might follow from that would all be capitalized.
Lastly, there is a measure of ethnocentrism at work (or, more properly, an equivalent case of "speciocentrism") whereby the quality of personhood is reserved mostly for ourselves and those like us, while outsiders, strangers, and foreigners are described in other terms, often by way of their foreignness. "Human" is a word that refers to a specific species, but it has also come to assume the quality of a sapient species in general, which the Mystics certainly are. Equivalent disparities exist in instances such as "white" versus "African American" and "godly" versus "Hindu." The bottom line is that, when it comes to the terms "human" and "Mystic" in regard to each other, what we are actually doing is describing ourselves (the humans) as people and the Mystics as, well, outsiders. The two terms are not conceptually equivalent, yet the juxtaposition is very common because of this egotistical tendency.
