I have the same problem. Run the Tower.exe, get a small unity window with the red ! in the upper left corner and a red progress bar at the bottom, then it closes. Modest PC: 3.4GHz Phenom II X4 965, 16GB RAM, 2GB GTX 950, Windows 10. no log file or other error info I can find.
The log file should be in
C:\Users\username\AppData\LocalLow\Nothke\Tower\Player.log, if it exists can you please send it to email@example.com?