Google Chrome closing tabs instead of quiting application

Solution 1:

That is the way most apps behave on Mac OS X.

The red x button in the corner of the screen closes the window, while choosing Quit from the menu or clicking Command+Q will close the app.

There is no way to "fix this" because that is the way the app is meant to behave.

Solution 2:

When you click the x Button, then the current window is getting closed.

A workaround to reopen the Tabs is via the Menu:

So when you close the window via the red x button, Chrome is still active. You can then click on the dock icon, and then go to File->Menu and click on Reopen Closed Tab. Alternatively you can use the keyboard shortcut Shift+Command+T to quickly reopen closed tabs.