Visual Novels like this where there are little to no choices of consequence are often described as "Kinetic Novels". I notice the tag isn't listed on this page, but the "Gameplay" section states "Cosy Cafe is more story than game, with choices mostly limited to interaction in sexual encounters," which fits the idea of a Kinetic Novel very closely.
Note that the term "KineticNovel" is actually a brand name of a japanese software developer which represents VNs which do not have any choices. Since it's actually a brand name you could potentially get into legal trouble ^^
Interactive VNs should mark their VNs as such, which most usually do as they include the fact of choices, alternative story lines etc in their description. There's not really a right or wrong here. Especially since the level of choices reaches from almost none to very extreme. Though the majority of VNs are mostly linear anyways and the "choices" they offer have cosmetic minute changes to some dialogs. What a lot of day / week cycle VNs offer is a somewhat "reordering" of certain events or parallel plot lines which are somewhat independent. So most are just illusions of choices anyways.
Many even argue if VNs count as games. I see VNs as an alternative media which exists somewhere between a book and a movie. It takes aspects from both to create a new experience.