It is real.
If you click on the link, you will see that the latest release as of today is 10.1.2
The update is legitimate and correct. Please refer:
The pop up that you are seeing is depicting what version of Adobe Reader is currently installed on your system. Once you have successfully updated to Reader 10.1.2, the dialog's title bar and the pop up message would change to reflect that you have Reader 10.1.2 installed.