That's really only designed for basic desktop access. I have no idea if it would be able to run games, but the problems you're likely to run into there are bandwidth, input lag, missing controls and an inability to see all of the interface clearly.
If you want to be able to play GalCiv 2 anywhere my suggestion would be to compromise and get/build a portable PC that you can easily take with you and hook up to a TV. I don't know if that would be within your immediate budget, but it would be a lot more playable that way.