This error is caused by Internet Connection Sharing (ICS) being enabled. You can disable ICS in either of two ways:

Per Adapter:

1. Click the Start button.
2. Click on Control Panel.
3. Click on View Network Status and Tasks
4. Click on Change adapter settings
5. Right-click the shared connection and choose Properties
6. Click the Sharing tab
7. Clear the Allow other network users to connect through this computer's Internet connection checkbox
8. Click OK

System Wide:

1. Click the Start button
2. Type: services.msc and press ENTER
3. Double-Click on Internet Connection Sharing (ICS)
4. Change Startup Type to Disabled (or in some cases you only need to press the "Stop" button).
5. Reboot the computer
6. You can now try reinstalling the AnyConnect VPN client again.