In a plot heavy story, I aim for 1000 words. This is actually far less than the average chapter in most real novels, but this is the Internet, and audiences here generally have much shorter attention spans. I like to keep my chapters bite-sized. To that end, it's also sometimes important to deviate from such word counts to ensure the chapter is bite-sized conceptually, as well. For instance, I've written chapters around 1500 words for longer scenes with no opportunity to break, and those as short as 600 for introductory scenes where avoiding info-dumping the reader is crucial.
In a game mode story, word count per chapter, of course, varies greatly. I can envision scenarios where just a few simple words would be justified. It's also possible for the need for a chapter displaying thousands of words to arise - such as a very comprehensive list or index - but I would cap actual prose at 2k.