The People app is tied to your Microsoft Account.
You will first need to log into your Outlook / Hotmail account using your web browser.
From there use the People app from within your web browser to import contacts by clicking "Manage" and then Import and then Gmail
You should see these instructions
You'll need to have first, logged onto your Gmail Account and export your Gmail Contacts to an Outlook.CSV file which you have saved to your computer.
Once that is complete then the Windows People App, after it has successfully sync'd should contain your Gmail Contacts that you've imported into your Microsoft Account.
Assuming you are using the same Microsoft Account locally on your machine, that you've used in the Web Browser.