According to the Wikipedia entry on high/low context cultureL
In a higher-context culture, many things are left unsaid, letting the
culture explain. Words and word choice become very important in
higher-context communication, since a few words can communicate a
complex message very effectively to an in-group (but less effectively
outside that group), while in a low-context culture, the communicator
needs to be much more explicit and the value of a single word is less
What this suggests in terms of UX/UI design is that depending on the type of communication you are providing to the end users (e.g. text, video, image, etc.), it needs to cater for the fact that some cultures require more explicit display or presentation of information in communication, while others allow context to guide the interpretation of the information presented.
I think it is important to break it down to different forms of communication, and perhaps also in different subject matter because of the cultural influence on these variables. For example, in Chinese the written characters provide rich information encoding lots of historical and cultural meaning and therefore require less characters to convey the same amount of information compared to English. However, if there are concepts in English without a parallel or equivalent translation then it becomes more wordy to explain something in Chinese compared to English.
What this means in general is that you need to get people who really understand the culture and context to design the content rather than rely on machine translation alone. It also means that specific iconography, image, colour and any visual or multimedia content needs to be reviewed rather than just applied directly between one culture and another. A classic example is the colours used for the stock exchange to represent gains or losses. In many Asian cultures red is an auspicious colour and used to represent gains, while in Western culture it is seen as a warning or dangerous colour and used to represent losses.
In terms of layout, I find the contrast between many Asian websites (Japan, Taiwan, Korea, China) and Western websites are in the density of information rather than the amount of content because there is probably a universal optimal character per line length that can be scanned by eye easily. You'll find the difference very obvious when you fly internationally and find some of the translation a bit quirky because they have had to squeeze the same amount of characters in a display space for all languages that they cater for, which is problematic if you translate from Chinese to English, or if you translate from English to German.