That's a 3rd party device "counterfeit", not from Microsoft. You should be able to get it to work, but it's not easy, especially with Windows 8. I'm about to install mine on my SP2 tonight, so I'll let you know. I think I've only ever written one review on Amazon, and it was for the "x360 wireless receiver" (a knockoff like your link). This should save you headaches:
I was almost going to return this, but I did finally get it to run on Windows 8. I found instructions, but that's not everything you need for Win8 -
WTFLOLOMGBBQ - View Article - The Xbox 360 Wireless controller saga
OK, this is the correct way to do it :
1) go to microsoft's website and get the installer package for wireless xbox thing for windows. (in my case, having win7 64bits, I got Xbox360_64Eng.exe)
2) Run the exe, install the stuff
3) connect the chinese rubbish, wait for windows to squeel about not finding the good driver
4) with winrar, extract to a directory the content of the installer file downloaded at step 1), go to sub-directory \xbox360\setup64\files\driver\win7 (adapt if 32bits and other than win7) and open up xusb21.inf with a file editor such as notepad, and replace (ctrl+H) all "PID_0719" strings by "PID_0219" ; save and close the file.
4a) For Windows 8, you need to disable security checks. Otherwise it will claim it's missing a hash and it's corrupted or tampered with....
It's possible to install the driver. Open a command prompt as an Administrator and run the following two commands:
bcdedit -set loadoptions DISABLE_INTEGRITY_CHECKS
bcdedit -set TESTSIGNING ON
Restart your computer. When you reboot, you'll be able to install any unsigned or test-signature-signed drivers without a hitch. The downside of this is that it leaves you open to security holes, so after you're done installing the driver, re-enable the integrity checks:
bcdedit -set loadoptions ENABLE_INTEGRITY_CHECKS
bcdedit -set TESTSIGNING OFF
After upgrading from Windows 7 a device driver no longer works - Super User
5) go to windows' device manager, you should find an "unknown device" floating around : that's the xbox dongle with no correct driver attached. Go to it's properties panel, use the "update driver" feature, and manually specify the subdirectory previously mentionned in step 4). Let windows find the patched driver. Done.
6) initial sync. press the button on the dongle. press the big X button on the xbox pad to make it come alive. press the sync button on the front of the xbox pad, let the stuff sync. there you go.
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So, I was finally able to get this to work and will keep it. It's a process though, and I feel ripped off by counterfeit goods.
Amazon.com: Customer Reviews: Xbox 360 Wireless Gaming Receiver Black