The refreshing of a linked Word document does not automatically happen as you have discovered and stated in the KB document. Amazingly this was reported in 2016 and ESRI have still (and I guess highly unlikely) not fixed it.
But all it not lost! I experimented with some code, running it in the Python console in Arcmap and I managed to get the layout linked object to refresh.
The trick is that the object must be named uniquely to identify it from all other graphic elements in the layout. I used a simple naming convention of "w0", I will explain the number portion a bit later.
First ensure you linked correctly as shown below (note checkbox tick):
Now ensure our linked word document object has the name "w0"
Now here is the code:
mxd = arcpy.mapping.MapDocument(r"CURRENT")
# Code assumes element is tagged with a consistent name that is different to all other names to identify it as a linked word document
# in this example the graphic element that is a linked word document is initially named w0
for elm in arcpy.mapping.ListLayoutElements(mxd,"GRAPHIC_ELEMENT","w*"):
name = elm.name # returns something like w1
# Get numeric portion of name and increment
n = int(name[1:])
n += 1
newname = "w" + str(n)
# Clone element and destroy old one
elm.clone(newname) # Creates a copy with the odd name of w1w2
# We need to correct the cloned name
oddname = name + newname
for elm2 in arcpy.mapping.ListLayoutElements(mxd,"GRAPHIC_ELEMENT",oddname):
elm2.name = newname
The code locates the element by name, increments the number portion so w0 becomes w1 , then clones it and deletes the old graphic element. Final step is to reset the name for the cloned element back to the format w1. The act of cloning and resetting its name has the effect of double clicking on the element to get it to refresh.
Note: I ran this from the python console within ArcMap and it worked well, I have not tried to run it outside an ArcMap session, that's for you to explore if need be.