That means eu4.exe never actually started, as writing those files is the first thing it does. They are still not there after running eu4.exe manually?And there's no folder call "logs" in Documents/Paradox Interactive/EU4. No settings.txt either.
Our similar game Crusader Kings 2 is free to play on Steam now. Does it work or have a similar problem?
Make a new Windows user on this machine and log into it with that. Do you get the same problems then?