Anyway, the point is not to argue whether your group fits the details of some definition of the word "cult" (discussions about the semantics of a word tend to be intellectually unproductive). The point is why it is generally considered harmful to be part of a cult and whether these reasons apply to your group as well.

I'm much happier to have the discussion on that level, but I think the primary argument you've put forward is the definition. If the definition isn't important enough to contest, it's not important enough to rest your argument on- and so you need to identify the causal mechanisms by which these behaviors are harmful.

The elements on the list that pertain to these rituals are "Use X to Y": "use chants to suppress doubt" and "use confessions to control by guilt." You notice the chants and confessions and are worried- but it's the Y that make cults harmful. If there's a group activity that includes confessions as a guilt-reducing measure, then that should be evidence against cultishness and harm, but it's not clear that you would see it that way. Notice the "if": I don't think the ritual as practiced is designed to reduce guilt for all participants, though it may do so for some participants.

Saying "I would be worried about sharing private information in a setting like this, and I think others should be worried as well" is a valuable contribution to the discussion, but "This smells like cultishness" is not. (In particular, it seems wise to include a warning that, while the group is composed of friends, three can keep a secret only if two are dead, in order to discourage people from sharing things it would be unwise to share even semi-privately.)

promote unearned loyalty

What would earned loyalty look like?