According to the microsoft website, the minimum system requirements for Zoo Tycoon 2 are:
A Pentium 733 megahertz (MHz) or higher processor.
One of the following operating systems:
Microsoft Windows 98 Second Edition
Microsoft Windows Millennium Edition (Me)
Microsoft Windows 2000
Microsoft Windows XP
Windows Vista
256 megabytes (MB) of RAM.
A hard disk with at least 900 MB of available space.
A 4x speed or higher CD drive.
A Direct3D-compatible super VGA graphics adaptor with at least 16 MB of Video RAM (VRAM).
A keyboard and a Microsoft mouse or compatible pointing device.
A sound card and speakers or headphones.
DirectX 9.0b or a later version.
Internet access to download optional content.
A supported graphics adaptor with at least 16 MB of memory.
Since your computer is capable of running Vista you should be all set to run Zoo Tycoon 2 as well. You can check the complete system specs of your machine through the following process:
Click Start, type dxdiag in the Start Search box, and then press ENTER.
If you are prompted for an administrator password or for a confirmation, type the password, or click Continue.
Click the System tab. Note the information for the processor and for the memory.
Click the Display tab. In the Device section, note the name of the video card and its Approx. Total Memory.
Click Exit.