Here is what you need to do:
1. Create an OU and move that computer into this OU.
2. In addition to your proxy setting in the User configuration you have done, go to the Computer Configuration>Settings>Administrative Templates>System>Group Policy>User Group Policy loopback processing mode>, click enable and select "replace" under mode. You have configured your proxy setting and enabled loopback processing GPO.
3. Link this GPO to the above OU
There, by default all authenctiated users will receive this GPO upon logon to the computer where you applied this GPO to. Yes, it's a User configuration GPO but linked to OU with Computer object. This is how Loopback GPO works. Of course there are other combination where you can leverage this type of GPO to be more flexible etc. But this is the most basic one you can test with.
Hope this help.