The particle が is referred to as a subject marker because that's what it is. It marks the subject of a sentence. That's its primary purpose.
Even in two of the four sentences you provided, it's quite clearly marking the subject of the verb います. Don't get confused because the "sister" and "cat" are both objects in the most natural English translation of those sentences - the basic meaning of います is "exist", and the sister/cat are clearly the subject of that action. A very literal English rendering of the two sentences would be "As for me, a sister exists." and "Beneath the table, a cat exists." - in both of which the noun marked by が is the subject.
It's true that there are a handful of adjectives such as 苦手 and 好き which use が in an unusual way which could be called an object role (though depending on the analysis, you can consider even these to be subjects), but these are an exception rather than the rule, and should be learned as such. In its standard usage, が unambiguously marks the subject of the sentence.
The main reason why calling が the "subject particle" can confuse people is because there's already another particle, は, which ends up marking the subject in most sentences. However, it's important not to learn は as a simple subject marker, because the "topic" is a more flexible concept which can actually fulfil numerous roles in a sentence. It's just that in the majority of cases, the topic doubles as the subject (and so the actual subject marker が is omitted).