The concept for something that combines AHKs scripting/automation functionality with the key remapping doesn't really exist on linux, because there isn't any need for it. You achieve the same result by calling the functionality present in a variety of different programs via a script or small program that links everything - this is the (superior) UNIX way.

Key remapping daemons such as keyd exist, as do a wide variety of extensible/scriptable window-managers/desktop-environments. Almost all of these will contain well documented interfaces and IPC methods which allow you to build anything you can imagine in the context of GUI window manipulation/management. If you're lazy, or don't have time to learn the syntax, any recent AI code helper will most likely oneshot your request - my 16 button mouse has various common GUI window management actions assigned to it(that you might expect something like AHK to handle), and only a couple took longer than a few minutes to implement.