It turned out that the downloaded file MUST be compressed as cab-file. That is:
[update]
newversion=2.1.0.37
localversion=client_app.exe
[files]
count=1
[file1]
url=http://myserver.com/client_app.ex_
newversion=2.1.0.37
localversion=client_app.exe
mandatory=1
[application]
appupdate=1
silentrestart=1
appname=client_app.exe
appcomps=client_app.ex_
And of course:
WebUpdate1.ExtractCAB:=True;