The recommended settings for Hitman Sniper Challenger are the following ones:
Core i5-680 3.6GHz / Athlon II X4 620
GeForce GTX 260 / Radeon HD 5770 1024MB
Windows 7 64
10 GB Free Space.
The game should run on lower machines as well, but if you didn't install the game properly, the it won't run. Make sure look in the installation directory for additional redistributables. This is mandatory for some games that won't run without those libraries.