The mail from Chad Horohoe didn't provide a patch file for updating from 1.27.2 to 1.27.3.
Topic on Project:Support desk
You can use the git pull command if you have SSH access (using putty, for example) to your mediawiki folder. More information can be found here.
I always use the complete tar archive and extract it over the old version. While this is not recommended for a major upgrade, this usually works just fine for minor upgrades like from 1.27.2 to 1.27.3.
Thanks for your suggestions!
I always use the patch like I described here - this works well and is very fast too.
In this case I downloaded both tar archives, extracted them, compared them with WinMerge and uploaded the changed files (only those). I didn't manage to create a patch file with WinMerge that would run without errors...