> this constant embeds two terms, exactly because this particular kinship term does not distinguish them
This isn't the case, any more than the English word 'aunt' embeds four terms (your father's sister, your mother's sister, your father's brother's wife, your mother's brother's wife). Plenty of languages distinguish between all four of these relationships. But the English term refers to what we see as a single concept - an aunt.
Most family words have translation difficulties like this. The concepts are usually more generic, more specific, or in some cases incomparable when moving between cultures. This also applies to many other words - even ones for very prosaic objects. The French have a single word which means "metallic object which has a particular shape in order to be able to turn something matching that shape", and they use additional qualifications to distinguish between a door-opening-shaped-metallic-turner and a bolt-undoing-shaped-metallic-turner.
The localization system seeks to avoid 2 things: that when an English speaker adds 'Mary (relationship: Aunt)' as a contact, they have to be asked "Is Mary actually your fathers-sister-aunt or your mothers-sister-aunt?" (Because that person would find it strange and unncessary.) Secondly that where possible, someone who has access to this information in another locale, doesn't see a low-quality translation, in particular one which makes no sense ("US English Kinship Relation �� Mary"), or which is misleading ("Mary is John's father's brother's wife? But I'm married to John's father's only brother!"). The right way to do this is to record a reasonable representation of the intended meaning in the source locale, and to translate into the destination locale. Since English also happens to be the language used for the code, the value "LabelContactRelationAunt" looks less complicated than this one, but it really isn't.
This can be seen by how it will be translated. In a locale where the English concepts encompasses two words, it might be rendered as "(Father-Aunt) or (Mother-Aunt)". In a locale where there are 4, 8 or more relationships which could be described in English as an aunt, they might use something intentionally less specific like "OlderFemaleRelativeNotAGrandmother" rather than a laundry list of possibilities. In others yet it might make sense to use the literal English word, or a contextualization like "Western 'Aunt'", if that's the easiest way to explain the relationship.
Nothing about this is unique to either English or Chinese.