x32 games on x64 Windows?

System Manufacturer/Model Number: The Cloud Windfoot Omega Build. Codename: Outpost
OS: Windows 7 Pro 64bit
CPU: Amd 550BE unlocked to Quadcore 3.1GHZ
Motherboard: GA-770TA-UD3 Rev 1.0
Memory: 4GB OCZ platinum 1333
Graphics Card: ATI 3850 512MB Asus
Sound Card: creative Xfi music
Monitor(s) Displays: samsung syncmaster T220+ Dell P780
Screen Resolution: 1680x1050, 1280x960
Keyboard: Microsoft natural ergonomic 4000
Mouse: Logitech G9
PSU: Ultra 500 watt
Case: some random case
Cooling: Coolmaster TX3
Hard Drives: WD 250GB segate 500GB
Internet Speed: Teksavvy 5Mbps down 700Kbps up
Other Info: there is a 80mm(8cm) intake fan on the side of the case and a 120mm(12cm) fan as exaust

System Manufacturer/Model Number: Custom Build
OS: W7 RTM Ultimate x64
CPU: Intel Q8400 @ 2.66GHZ
Motherboard: Gigabyte GA-EG45M-UD2H
Memory: 4GB DDR2-800
Graphics Card: Gainward GTS 450 GLH 1GB Edition
Sound Card: Integrated 8 Channel
Monitor(s) Displays: AOC 23.6 Inch Widescreen LCD
Screen Resolution: 1920x1080
Keyboard: HP SK-2960 Multimedia Keyboard
Mouse: Logitech M350 Wireless Gaming Mouse
PSU: Apevia Java Power 500W
Case: Cooler Master HAF 922 Black
Cooling: Stock Intel CPU Fan
Hard Drives: Seagate 500GB Internal Western Digital 1TB Internal Hitachi 1TB External
Internet Speed: 1.5MB