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I wonder if there's anyone out there who can read a non-alphabetic language (e.g. Chinese) but doesn't even know how to pronounce what they're reading.This is actually how many people learn Japanese. They get an anki deck with kanji and their meanings and learn from that. The decks might have some pronunciations of the kanji, but typically not all of the pronunciations (or people don't learn them). This leads to a situation where they can read text and understand most (all?) of it, but would have difficulty reading it out loud.
Japanese kanji (and Chinese hanzi) are logographic. Each symbol denotes a word or a phrase and depending on the context it can have a different pronunciation, however the meanings generally stay rather similar.