the only way to play a *.DEM file is the DOD:S engine itself,no other player will play a demo.
first things first.
what u should do is to copy the dem file into the proper folder..(dod)
the route should be something like this:
C:\Program Files\Steam\steamapps\YOURUSERNAMEHERE\day of defeat source\dod
to play the file,open the console,to do so,type "~" (no quotes)
once ur there,type "playdemo DEMONAMEHERE" (AGAIN,NO QUOTES)
example:
playdemo KC.dem
let me know if u fail again