Is it possible to run games made with Adobe Director (shockwave player) in Facebook?
Yes.
Applications inside of Facebook can be rendered in two ways. FBML or inside of an iFrame. In the case of FBML you can embed FLV, SWF, and silverlight files. In the case of an iFrame you can render anything you want. You can choose the type of application canvas on the developer settings for the application.
Each of the options has certain benefits and limitations, but if you're only concerned with embedding a shockwave game then this shouldn't matter.