In your question, the word "like" is being used similarly to "such as" or "for example."
While "such as" can be a better choice when you want to include a list of examples rather than compare them, "like" appears to be the most appropriate choice for your example, as it is comparing a list of other languages to English.
Alternatively, the writer could have used "e.g." (meaning "for example") to further clarify that it is a list of languages with instances differing from English.
If we rephrase it with "e.g.," you may see how "like" works here.
"There is no special preposition in English to express the idea of being at somebody's home (e.g., "chez" in French, "bei" in German, "hos" in Danish/Swedish/Norwegian, etc).