Jeffrey Zeldman said (in 2015):
“Mobile is today’s first screen. So design responsively, focusing on content and structure first. Websites and apps alike should remove distractions and let people interact as directly as possible with content. 90 percent of design is typography. And the other 90 percent is whitespace.”
(Zeldman knows his shit. He was one of the most influential designers and standards-setters for the early web, e.g., founder of the Web Standards Project, which was instrumental in helping us escape the minefield of browser-specific customizations in the late 90s).
Most of the principles of good typography apply anywhere that type can be used, from books to billboards to websites to mobile games. Typography as a discipline is thousands of years old, and based in the fundamentals of human perception. We know how humans read. Typography is the practically application of that knowledge.
There was a brief period where coolness and aesthetic appeal on the web trumped good typography principles (e.g., again, the Arctic Adventure site). Most of that has settled down, though, and most sites have reverted to simple and common standards.
typography is generally involved with any text, many of these are standards that have existed for hundreds of years and still exist on computers