If you want some website to be in their own window, visit them in Chrome and go to 3 dot menu and Add to home screen. Basically similar as on desktop, with the taskbar/desktop icon.
Hm, that's odd, I've added Strava to homescreen since the Android app runs a constant GoogleNowAuth service and wasting resources. It runs in it's own window. Although I use the Chrome Beta 52, maybe there's some differences.