Capitonyms - do they occur in other languages?

I dispute the “very different thing”; capitonyms are a special case of homographs. The Wiki page you link to even says so explicitly (“A capitonym is a form of homograph and – when the two forms are pronounced differently – also of heteronym.”). I think the definition given on the Wiki page (which you quoted in the OP) is misleading, since there is apparently no actual requirement that capitonyms be one word with two meanings, and many examples that it lists are the opposite, two distinct words that share a spelling. (Or maybe there is inconsistent use of “word” as a unit of language and “word” as a unit of text…)

In terms of your question re whether they exist in other languages, I think my answer stands: all written languages have homographs, so any (alphabetical) language that uses capitalization to mark word categories will have them. The more a language relies on capitalization as a category marker, the more likely it would seem to have plentiful capitonyms; Mops has given some German examples, and I think German will be a fertile source because of its very broad use of capitalization to mark nouns.

In any case, the term “capitonym” seems to be something made up for a “humorous things about the English language” type of book (specifically, Richard Lederer, Crazy English) and I’m not convinced it is a particularly useful distinction vs just “homograph”. The capitalization angle is an artifact of writing conventions; in “RIOTING RESTAURANT PATRONS IN CHINA CAUSE MASSIVE CHINA BREAKAGE”, there is no capitalization difference but the China/china meaning is still different.