I'm having the same issue. My FFXIV is a Steam installation. I tried uninstalling/installing, deleting files in the my games folders, manually clicking on ffxivupdater.exe within the my games folder, and so on to no avail.

Whatever I do, I keep on getting a "FFIXV Launcher Error". The message I get is this:

Unable to complete version update.
[30435][30415][5][19900][5]

I had no such issue until now, so this is definitely related to Patch 5.3.