Running a graphical display is not one of Galileo's strong areas. Some might say it is a weakness.
Out of the box, the galileo has no Video output. I have heard of some people wanting to connect a PCI-E graphics card to the mPCI-E connector on the bottom of the board. As far as I know, no one has been able to get that working yet. I think they were trying with the Yocto Linux image, and it is probably easier to enable the video on one of the debian images that people have recently made.
One person has gotten a TFT to work with Linux.
That is a touch screen (not sure if the touch is hooked up to software??) but it is much smaller than the table you give as an example. You should look at that thread.
I think your question is so generic, that no one can really give you an answer. However, I think I can give you some ideas. Consider what you want to do with the LCD. The example you linked to involved manipulating objects with a touch screen. This means input latency is very important, however things like video decoding doesn't matter. Do you need to support video as well? Think about other scenarios you want to support as your solution will greatly depend on this.
Something like the Gameduino is object-based. The FPGA handles the video support so it leaves you to selecting a computer that doesn't need any video support that can be more targeted to the other parts of your solution. A beagle-bone black or PI might also be a good choice as they both have graphics chips with HDMI support and can handle video. None of these help if you don't have a LCD with HDMI, DVI or VGA input.
So I recommend finding a few LCD and touch panel options first. Figure out what bus and connectors they have and what it takes to drive them before deciding on a computer. If you are fortunate you can find something that has a pretty standard PC interface it will be a much easier project, however Galileo is very likely not a good choice for that. If you find something that you can control over PCIe, USB or a simple I2C or SPI bus, then Galileo might be fine.