Chinglish, as with all pidgin dialects, is an interesting phenomenon. The most basic definition would be to describe it as the fusion of English vocabulary with Chinese grammar. All fine and very widespread, but the one thing you don’t see so much of is the conflation of Chinese vocabulary with English grammar. Take these two examples, which you could hear from an expatriate in China,
“Do you know where I can buy a chongzhi card around here?” Rather than, “Do you know where I can I buy a top-up card around here?”
In English-speaking countries, this type of mixing is rare if not non-existent, because there is no need for it. In other words, if an English word already exists, it’ll usually be used in favour of a foreign alternative. But the thing about loanwords is that when they have been needed and used, they have almost always been borrowed in the original form without too much alteration. English is not a language that relies heavily on translation nor makes radical changes to loanwords to suit the English sound scheme or lexicon.
Nevertheless, in the current era of globalization, it is comparatively difficult for a Chinese loanword to come into the English vernacular. This is because Chinese phonology is so far removed that words tend to sound incongruent without a major corruption to anglicize them / mangle them. Syntactic forms, though, have a slightly easier time finding their way into the idiolects and idiom of English speakers – which is possibly a subject for another post.
To my mind, there is one import into English that has come not in the form of a loan word nor a calque, but in the form of a non-native translation. This word is ‘bubble tea’. For the uninitiated, bubble tea is a very sweet and weak variant of regular black tea with milk and sugar. The special addition being a number of soft and chewy tapioca balls which are sucked up through the straw and eaten at the end of the drink. It became popular in Taiwan in the late 1980s and now is a common feature all over the sinosphere and beyond.
The tapioca balls are called bobà in Chinese and I think it’s a safe speculation to presume that early purveyors of the drink in Taiwan marketed it as ‘bubble tea’ in the English translations on their menus, and that someone settled on this translation because it is a convenient and analogous homophone.  Possibly from this point, as its popularity mushroomed, ‘bubble’ became generally adopted as the nominal English term for the tea, in competition with the fairly common alternative, ‘Pearl Tea’. 
If this is explanation is true, then the interesting thing is that ‘bubble tea’ may be the only English word that is indigenously inspired by Chinese speakers, with the notable exception of proper nouns, that is, the capitlaized names of individuals, places, companies, etc. Thus we could say that bubble tea is unique by not being unique.
A friend of mine alerted me to the imperative phrase ‘chop chop’ as another an anglicization. But the important difference here is that it was coined by colonial-era English speakers who substituted the Chinese for ‘quick’ (kuai) with ‘chop’ (which also meant quick in the sailor-speak of old), making it a calque. ‘Bubble tea’ on the other hand, may be one of the only instances of non-loanword, non-proper noun, English vocabulary being directly generated by second-language speakers. 
So why would this come about? Firstly, Chinese dialects have a tendency to transliterate foreign words, much in the same way, but not on the same scale, as the Japanese do. This is in preference to finding a native translation or calque, which perhaps the mainland Chinese tend to do a bit more so. It’s simply a question of style.
Secondly, the word ‘boba’ is highly idiomatic, meaning literally ‘mighty wave’ and thus it is rather difficult to translate. In this case, the easy option of ‘bubble’ makes good sense both semantically and phonologically.
But perhaps this conjecture asks a larger question, and that is, will we see ‘reverse chinglish’ or straight chinglish coming into English in the future? I think the answer to that lies in the capacity of the Chinese to invent original concepts and crucially, to translate them into English before native speakers do. However, the paucity of such examples suggests that it will be a long way down to road before such interconnectedness and innovation become a reality. 
1. The main candidate for the invention of the beverage is the Chun Shui Tang Teahouse in Taichung.
2. ‘Bubble Tea’ outnumbers ‘Pearl Tea’ on Google search results by a very large margin.
3. It’s not easy to think of other examples. ‘Walkman’ springs to mind, which again is a proper name, although it has undergone the classic process of trade mark genericization.
4. See ‘The China Question‘