Yes, 「というのか」usually marks a rhetorical question, but here the sentence ending particle (終助詞) is not 「か」「の」or「だ」. It is a compound (連語) of two particles 「か」「な」. 「かな」is a word all its own, usually translating as "I wonder". 「かな」shouldn't be confused with 「か」.
It makes sense the speaker uses かな in her monologue, much as how people say "I wonder" talking to themselves, with or without listeners. 「って」is a colloquialized 「と」. 「の」is a nominalizer. Nominalization is really common in Japanese. I would interpret this「っていうのかな」as summarizing what's before it and then expressing something like "that thing, hmm..." or "just like that..." In fact, if I were to translate this sentence I don't think I would translate that part, at least not as a sentence ending. I would probably use phrases such as "I heard..." or "the feeling that" to convey the hesitation and indirectness.