Which version of CrossOver Games are you using? We had a problem with the Install button, but it should be fixed in CrossOver Games 7.2.
With respect to mods, I am only seeing the "Visit Website" link, too. That's what you see if you browse the Steam store using a web browser, too. So, that seems like a deliberate change in Steam. I'm seeing proper "Install" buttons on things like demos, and they work.
Oh, wait, I found a mod with an Install Game button: Eternal Silence. This does the right thing in Steam, as far as I can see. You can also run the command "start steam://store/17550" in CrossOver's Run Command (on Mac) or Run Windows Command (on Linux) dialog to visit that mod's page. You can run the command "start steam://install/17550" to install it.