I think this Japanese couple lives in Perth. Anyway:
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風呂 is probably the really tricky one, I know it means bath from reading manga. I like this guy's reply:
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Which is actually pretty profound if you think about it. To be fair if you translate local dialects word by word into written Chinese a lot of times it does look just like ancient Chinese. As a Shanghainese for example if I were to tell my wife I'll be back for dinner tonight at 7PM it will be something like:
"我
今朝夜头七点钟回来吃饭”
The mundane answer is that written Japanese literally evolved from Classical Chinese. Even as recent as Meiji era, formal Japanese writing is written in a form that can be mechanically translated into something resembling Classical Chinese. This no longer quite hold with modern written Japanese, but that explains why it's even possible for people to do this in the first place.
The pseudo-Chinese form of Japanese is not quite "just strip out kana and call it a day". The writer basically had to go out of their way to pick sino-xenic vocabulary, and render a lot of stuff that would be normally be written in kana into kanji. The translation required (which is more or less the inverse of the process that turns Classical Chinese into something parseable in Japanese) gives the impression that modern written Japanese resembles Classical Chinese when it really doesn't, at least not without some serious eye-squinting.
Not too bad for something that originally came from a certain gay p*rn's appreciation community, I suppose. Incidentally, this is why the corpus of Pseudo-Chinese contains a suspicious amount of "射爆" and "谢谢茄子".
As for local dialect looking like Classical Chinese when written out, I guess that just comes down to natural evolution of language, where some dialects are more conservative than others.
Of course, this invite the sort of w*nkfest such as "hurr durr my dialect retains more sounds and features from þe olde Chinese, therefore I am real Chinese, and you are barbarian and not real Chinese huehuehue" from a certain group of people.