The page https://developer.chrome.com/multidevice/android/installtohomescreen states the following:

"How can I detect if the app is running as an installed app?
    You can’t, directly."

I'd argue that that is no longer true, now that display-mode:standalone can be detected (https://developers.google.com/web/updates/2015/10/display-mode). Seeing how https://developer.chrome.com/multidevice/android/installtohomescreen is the #1 hit for "chrome add to homescreen" (without quotes) on Google, I think a reference to detection using display-mode:standalone would benefit the internet.

Also, I got to this bug tracker by clicking "Report a content bug" on the bottom of https://developer.chrome.com/multidevice/android/installtohomescreen, but was presented a "Defect on Windows" bug template. This doesn't make a lot of sense, and I couldn't find a template for a documentation content bug.