It's not easy to ignore whether or not this is a good idea, but I will do my best to suppress my need to facepalm and concentrate on the pure technical viability.
PDF has Javascript support to add interactive elements to a document. This could be used to implement simple games. But you can't just take a game you implemented in some other technology and embed it in the PDF file. No, not even a browser-based game you developed in Javascript. HTML-Javascript and PDF-Javascript use the same syntax, but have a completely different set of global objects and functions. You will have to use what the PDF API offers you and develop the game specifically for this purpose, and it's not an API intended for game development.
For more information, I recommend the Acrobat JavaScript Scripting Guide by Adobe.
Microsoft Office also has VBA macros which allow the same. There is also support for COM and ActiveX elements, which allows to interface with different technologies, so in some cases it might even be possible to get a game implemented in a different technology to play inside a .docx document. But any sane company would not allow to play macros from files with untrusted origin for security reasons: they allow to do some quite evil things.