Not trying to be offensive to the vgchartz posters, but most of them have provided you with a lot of useless opinions with no real solid reasons.
Here are the reasons I think this computer is a bad choice for gaming:
1) The graphics card is a 9500M GT. Money could be better spent getting a better graphics card.
1a) From the pictures I received upon googling the card, It indicates to me that the card is non-removeable/not-upgradeable. This is bad for future upgradability.
source: http://images.google.com/images?hl=en&client=safari&rls=en&um=1&q=geoforce+9500m+gt&sa=N&start=0&ndsp=21
Notice that the only pictures of cards are the actual 9500 GT, which is different. The 9500M GT is a 'notebook' graphics card and those tend to be non-removeable.
1b) A 9500 series card for Nvidia is some-what midrange. Good for decent graphics, but not made for intense video games.
This chart compares graphic card performance: http://www.tomshardware.com/charts/gaming-graphics-cards-charts-2009-high-quality/3DMark06-v1.1.0-3DMark-Score,1468.html
The 9500M GT is a bit more powerful than the 8600 GT, but not as powerful as the 8800 GT. You can see those are towards the bottom of the chart.
2) The computer system is integrated into the monitor. This computer's purpose seems to have been geared around playing blue-ray on the monitor, which this system would excel at. However, there is a trade off with cooling and non-standard parts compared to a tower based PC.
Here is a more detailed list of the computer's specifications: http://reviews.cnet.com/desktops/sony-vaio-vgc-rt150y/4507-3118_7-33240538.html?tag=mncol;psum
If you have any more specific questions, fire away.
edit: I re-read the above posts. Perhaps the "most of them have provided you with a lot of useless opinions with no real solid reasons." was uncalled for.