I now see in Is the native ArcGIS database capable of doing generalized data manipulation?, to which I also responded, but that I didn't know was related to this one, that you attempt to run an UPDATE SQL statement via the Query Layer interface. That is not possible. Query Layers in ArcGIS are read-only.
You either need to buy an ArcGIS for Server license and upgrade your database to be an ESRI Enterprise Geodatabase, or, if you can live with the limitations of a Microsoft SQL Server Express database (10GB max, one core), you could install that and have a free Desktop Geodatabase, because that is part of your ArcGIS for Home Use license. Unfortunately, Desktop Geodatabases are only supported in SQL Server Express, not in any of the other geodatabases supported by ArcGIS.
I explained how to install a Desktop Geodatabase here: https://geonet.esri.com/message/118404#comment-118404
And I recently noticed ESRI finally seems to have better documented this as well, at least I can't remember seeing these pages before:
As LR1234567 writes, QGIS may be a better option in your case.
I also wonder why you actually wish to do this type of SQL update through a GIS. If there is no real spatial component to your question, doing it command line in PostGIS is probably the way to go.
You generally resort to GIS when most of your manipulations are spatial, as the required SQL to do it could quickly become unwieldy.