First things first, OpenGL is not a library. It's a drawing API for talking with the graphics drivers to make the GPU do nice things.
As such, OpenGL comes as part of the graphics drivers. Unfortunately Microsoft decided that they don't like OpenGL and would not ship drivers fully equipped with modern OpenGL profiles through Windows' built in driver update mechanism. Oh, yes, they added legacy support for OpenGL-1.4 (which was specified in 2002), thank you very much.
So you have to take things into your own hands. First step: Go to the control panel and open the Hardware Manager. In the section
Graphics Cards you'll find the name of your GPU. Most likely it will be made by one of Intel, Nvidia, AMD or ATI.
Depending on who made it you can find the drivers on:
Select the drivers appropriate for your system, download and install them.
or how to check current version.
Since OpenGL is not a library the truly limiting factor is the GPU in your system. If your GPU doesn't OpenGL-2 you're SOL. However you'd have a really, really old GPU for that and Windows-8 would not even boot on a system with such a GPU that old. Update your GPU drivers and you should be fine.
Do I need a separate OpenGL installation/upgrade or has it to be included into my graphic card driver? Where can I get it?
OpenGL can't be "upgraded", and it must be included with your graphics driver. OpenGL exposes GPU hardware capabilities to the operating system. If your GPU hardware were more capable, it could support later revisions of OpenGL on Windows XP with a newer AMD Catalyst device driver package. But your hardware is at least 6 or 7 years too old to support that.
Now, emulation of any revision of OpenGL on the CPU is possible. However, the reason that GPUs exist is that they can compute graphics operations much faster than a CPU of the same generation. For any game, whether it's simple 2D or not, my rule of thumb is, you can run its 3d renderer in software with a high-end CPU from 10 years in the future. So for an OpenGL 2.1 game, it would've had to have been released no earlier than July 2006 (since that's when OpenGL 2.1 itself was finalized), meaning we could start to see playable framerates (30 - 60 fps) when rendered in software with an optimized OpenGL 2.1 implementation on a current-gen CPU.
Of course, on current-gen Intel and AMD CPUs, we almost always have an on-die GPU that's more than capable of running an OpenGL 2.1 game, anyway, so...
Indeed, the mesa3d project maintains such an optimized software renderer as part of its project, but support for Windows is an afterthought, and building it is a bear. Additionally, they don't guarantee good performance or even correct behavior unless your CPU has SSE2 and SSSE3 and SSE4.1. A CPU contemporaneous with a motherboard with an AGP slot (something like a Pentium 4, yeah?) may have SSE2, but probably not the others.
Unless you have a high-end, modern CPU from the past 3-4 years, like a Core i7 3770K or better, you're not going to be able to emulate OpenGL 2.1 in software at a playable framerate. Not even for a very old game. Given that your CPU is probably as ancient as your GPU, you're completely out of luck. That GPU is completely "fixed-function" and does not support user-submitted code. OpenGL 2.1 runs almost any arbitrary operations on the GPU when submitted as a fragment shader. You can buy an ARM System on Chip for $1 with a GPU 1000x better than that RV280.
You're better off upgrading.
Here is the procedure:
Verify your OpenGL version with this program: OpenGL Extension Viewer
Go to OpenGL getting started page -- select your graphics card vender, and go to their website to download the latest driver.
In Intel's case:
Automatically get your driver version checked from here (Java required)
If your driver is older, it will automatically provide you the link to the newer version.
Download and install it.