You need to configure your Steam app to run the GameInput installer when installing the Steam app. I'm no expert on this as we do not publish content to Steam ourselves, but it looks like the way to do that is with install scripts.
it turns out to be that he can use gamepad without any issue while I cannot
This is probably because they had GameInput already installed by something else, whereas you did not. You need to run the GameInput installer to make sure it is installed.
when I checked another C3 game(which gamepad is also working for my laptop) file downloaded from Steam, there is no "scirra-gameinput-x64.ext.dll" in the package
There have been some recent changes to support the Steam Overlay. Older games may either work differently or not support the overlay.