It looks like Google Chrome for Windows uses the regular Windows folder icon - they look the same:
My guess is that on Linux, it's intentionally built with a flat icon because every distro ships different icon themes.
Historically, I do remember when Chromium/Chrome had icons like this on both platforms:
The source code (and its version control history) for Chromium will have all the answers. 
From quickly looking at the Chromium GitHub mirror of the source code, I couldn't find our 
icon. I found the Windows 
, Mac 
, and the old one 
in this folder:
Theoretically, since Chrome is based on GTK, the developers could add some code to get the folder icon from the current theme, but I don't know the codebase so it might not be as straightforward as that.
Somewhere in the source code will have the answer. 