When you look at the GPU standards at least for Nvidia u will learn what (GTS 360M) those letters mean. M is a mobile on board proc type GPU. Usually very limited especially for game play. The GTS is another give away at the type of GPU the S in GTS. Usually base model no frills but yes it will play your DVDs/videos gfx card. GT has better clock speeds and usually a bump in the interface bandwidth speed so example GTS has 256/128 bit speed. GT may have 512/256 bit speed. The GTX units will usually jump to 1GB/256 and then it just gets even more ridiculous from there with over clocking blah blah. I have a GTX 260 M in my laptop. It plays the game pretty well. Not compared to the actual GTX 260 cards you can put in an actual rig though.

Just some info if you go to look and buy a new LT. Best bet, try dropping the settings a little more in the config for FFXIV and find a nice compromise. GL!