Chinese also is a great language for puns. I was in Taipei a few weeks ago and saw a restaurant named 糖朝 (tangchao, Sugar Dynasty), when most people would expect to see 唐朝 (tangchao, Tang Dynasty).
In addition, many cultural sayings are based off "puns." For example, 年年有餘 (nian nian you yu, year after year there will be a surplus) is a common saying during the Chinese New Year. However, many families eat fish (魚, yu, fish) during the Chinese New Year because it sounds like surplus. And so, 年年有餘 is sometimes rendered 年年有魚 (nian nian you yu, year after year there will be fish).
There's an entire type of Chinese comedy which is roughly translatable as homophone puns (相声). Few non native speakers ever get good enough to do it.
In fact when I was watching the CCTV New year broadcast in English 7 or so years back, the translation and subtitles basically just gave up for all of the crosstalk segments. They just put a banner underneath saying basically "this is crosstalk now, sorry we can't translate it because it's too hard".
I had a conversation with someone in Taipei once, asking them if they had puns in Mandarin, after explaining what's puns were he said "oh no", which mystified me because just about every word has different meanings by changing the tone on the vowel ... When I asked about that it was "oh yes we do that all the time"
Chinese here, I agree that it is very easy to have puns in Chinese. But I don't think Chinese find puns very humorous in general (probably it is too easy?), is it more often used to make blessing or satirical phrases.
I've read about the 10 Mythical Creatures of Baidu[0] a few times, and while my Mandarin is too poor to have gotten any of the jokes without explanation, it seems like it would have been quite funny to run across any in the wild.
The Chinese language great for puns not only because so many characters sound the same, with tons of idioms understood nationwide. Because the language is character based, abbreviations of words are made of full characters and may have their own meanings. As someone graduating from the department of computer science, the most classic joke is to shorten the name of the department into "whorehouse". (计算机学院 ji4 suan4 ji1 xue2 yuan4 => 计院 ji4 yuan4 ~ 妓院 ji4 yuan4)
In addition, many cultural sayings are based off "puns." For example, 年年有餘 (nian nian you yu, year after year there will be a surplus) is a common saying during the Chinese New Year. However, many families eat fish (魚, yu, fish) during the Chinese New Year because it sounds like surplus. And so, 年年有餘 is sometimes rendered 年年有魚 (nian nian you yu, year after year there will be fish).