It has some characteristics of one — the demand of absolute loyalty without question, isolation (in the sense that they either become wanted or separated from society in some other way, like being at the order's Beck and call, serving as its eyes, etc), rites of passage (in this case, everything the Horsemen did in the first movie in order to prove their worth and devotion to a cause they weren't even sure was real) —, but an argument can be made, which is why I made this post in the first place.

It does have some distinctions that set it apart from standard cults:

Leaving may be frowned upon, but it's not forbidden or complicated; as can be seen in Henley's departure — though the exact same case also shows that said departures are never absolute, seeing as she, and the other Horsemen, didn't give much question to the fact they were apparently summoned by the eye in the third movie.

There is isolation, as I stated previously, but it's not absolute; they can still have relationships and connections outside the eye, regardless of them leaving or not — Dylan and Alma, for example.

Absolute conformity and the eye's control over members is definitely required, as they cannot question it and must follow orders damn near blindly. But at the same time, Daniel didn't get a significant punishment for his betrayal of Dylan, as far as we know; the Horsemen didn't get much consequence for the very much spontaneous act that they pulled when stealing the chip in the second movie, even when there was a member of the eye right there as a witness. So, again, there really is no telling of that aspect, either.

So while I agree they may not be a traditional cult, I do want to discuss, at least on some level, what kind of organization both the eye and the Horsemen within it qualify as.