It would certainly fit however this card is a number of years old and would not suit your criteria of running at the highest settings.
However what you could do is use the 8800GT for now and then save up for a new graphics card in a month or two, as the computer will be easily upgradeable for that purpose. If you wanted to save a few dollars again, you could drop the 750GB SATA hard drive which I included to be used as a data drive - you likely have a SATA drive in your current build which could be used in place, as long as it is in good running condition. Feel free to run a diagnostic on your current drive and if it passes in good health, then you could do that for now also.
Also another option to drop the price a bit further would be to go for 8GB RAM now, running 2x 4GB modules such as this kit: http://www.newegg.co...N82E16820231544
You could easily add another kit down the track to have 16GB total however 8GB would likely be plenty enough for the time being.