The configuration should work in either setting. If you'd like to deploy the GPO to specific users regardless of the machine they are using, you would use the User Configuration. If you want to deploy to a specific set of machines regardless of the users logging in to them, use the Computer Configuration.
I would personally use the computer configuration to make sure only end user machines are receiving the policy. You then want to link it to an OU containing some or all of the machines you are deploying to. Here is the policy setting that you should be using.
Computer (or User) Configuration -> Policies -> Administrative Templates -> Google -> Google Chrome -> Startup, Home page, and New Tab page -> URLs to open on startup
If you are still having issues after verifying everything, I would double check the browser versions and the ADMX templates.