Yes, it seems that way I agree. But the definition uses the work "kind" implying a grouping or set. So this infers that the unique-ness may be confined to a property the object has. Or in other words, a object can be both unique, and alike something else at the same time.Unique: Adjective: Being the only one of its kind; unlike anything else:
So either it is or it isn't. Seems pretty straightforward to me.
An example given on line of unique:
"Each person's signature is unique"
Ok, in the context of signatures, they are unique. But in the context of what are they, they are all the same, they are signatures.
So its possible that something could be unique in one or more categories. So like infinity, it would at first sight seem there was one, but on closer examination its possible to have higher orders of uniqueness, so its possible that way for objects to possess more or less of the property.