I'm pretty sure your system (excluding monitor) will be drawing less than 750 Watts from the AC power plug while you're gaming.
The LG Flatron W1934S has a typical power consumption of 36 Watts according to LG's documentation.
Newegg's online power supply calculator tends to overestimate the power requirements because they are trying to sell you a more expensive power supply.
That UPS, that you've linked to, should work just fine with the system and monitor plugged into it.
The power supplies' that have a problem with simulated sine wave UPS' will usually result in the UPS producing characteristic gurgling sounds and shut down in half a minute after switching over to battery operation.
You would then have to consider using this one instead:http://www.newegg.com/Product/Product.aspx?Item=N82E16842102134