Theoretically, if your TV had a VGA port (which some do), then I think you could use your hypothetical HDTV as a monitor for your theoretical Mini and watch it that way.
Also, if, say, you had a product that would write viewable DVDs of AVI movies, such as Toast, then it may be possible to write this movie onto a hypothetical DVD to play in a DVD player that may or may not actually be connected to this potentially non-existent television.