Yeah, it’s a bit of a reoccuring problem with Bunpro that they don’t use literal translations. A literal translation, like you’ve said would be something like:
”That person is a person who’s the equivalent of a relative to me."
Which we wouldn’t say in English, hence the unsatifactory translation by Bunpro.
I’d also like to point out that the Japanese sentence itself 「その人は私の親戚に当たる人です」feels a bit redundant and unnatural (just like the literal English translation.) A better standalone sentence would be 「その人は私の親戚に当たります。」Without the broader context, it’s hard to understand why it’s written the way it is.
But, you know, take the English “equivalent to” in the literal translation. I suppose it could similarly mean that the person literally is a relative, or it could mean that they fulfill the role of relative. The vibes I get is something along the lines of “I consider that person a relative, our relationship is like that of relatives, but I’m not sure, or it’s too complicated to explain, how exactly we are related (maybe a distant cousin or someone married into the family).”
In any case, what you should keep in mind is that に当たる’s translation is heavily context driven (there isn’t a direct English equivalent to this grammar concept). It is used over です in typically formal and written contexts, when explaining or clarifying a relationship that isn’t immediately obvious (as opposed to using です to make a simple, factual statement).