Why doesn't Google integrate its services like Google+ and Gmail into Google Chrome?

Google+ and Gmail are web applications designed to work in any browser with an internet connection.   Chrome is software that is loaded locally on a computer or device.  It's a browser. 

In line with making Gmail and Google+ accessible to all, Google has made sure they are not platform, device, or even browser specific.

Instead, they let the user decide on browser integration.  You can use the Chrome Web Store to install the Gmail app or several other extensions to integrate Gmail and other services with the Chrome browser.