Ambiguous means two (or more) different possible meanings, not two conflicting meanings. No ambiguity here. Just a possible error by Apple.
You correctly interprete both statements as not applying to your situation ("I don't fall in this category" and "I also don't fall into this exception"). But then you go on to conclude "Since I don't qualify for any exemptions listed, I would assume I do have to implement Apple Sign On." Why do you do that? You need to fall into a 'listed exemption' only if you fall into the original "must also offer" category. So unless Apple incorrectly included the word "exclusively" in the guideline you, unambiguously, do not need to use Apple Sign In.
But.....IMHO they incorrectly included the word "exclusively" in that "(a)pps that exclusively use" statement and, if so, and again unambiguously, you must use Apple Sign In if you use a third-party or social login system. (Note - they use a singular 'a third-party' in the first 'exclusivity' so that's another error - do you escape the requirement by using both Google and Facebook?) This interpretation is driven by that 'exclusively' in the first exemption which doesn't seem to make any sense otherwise.
But... I may be wrong. The first exemption, in fact, does make sense, and is required when read by Facebook, Google and other social login services. Therefore, perhaps that first exemption is meant to apply only to a social login company that only uses its own login system and would otherwise be required to use Apple Login. All others would not fall into the original 'must also offer' since they do not 'exclusively use a ..social login'.
It's not a question of ambiguity. It's a question of whether or not there is an error in the guideline as written. Albeit, your choice is ambiguous; don't use Apple Sign In and quote the Guidelines back to Apple if you get rejected (I'm not suggesting that will work) or use Apple Login. We shall see whether or not Apple edits their guidelines to actually include your use case in the future.