If you think you are going to run an ethernet cable between the TV and the Mini and have it act like a video cable, you are mistaken.
If the Vizio TV has a built in media player and you want to use that to play files that are shared from the mini, that would work depending on file types. I don't know if the Vizio has such a player, but it might. Devices that allow file sharing like that often use DLNA, which is not built into OS X, but you can find software that could be installed on the Mini to support it.
The thing that the ATV would add for you would be the ability to play DRMed iTunes Content out of your iTunes library that's shared from the Mini. It would also allow you to use AirPlay from an iOS device to send content to the TV from Apps. The iTunes content is the big thing though.