Check your connection with Steam and ensure the connection is working correctly.
Run the secondary installers required by this game :
1. Exit Steam entirely.

2. Browse to your Stronghold 3 installation folder (Usually C:\Program files\Steam\Steamapps\common\stronghold3\)

Run the following installers:

...\Steamapps\common\stronghold3\resources\directx \DXSETUP.exe
...\Steamapps\common\stronghold3\resources\dotNetF x40\dotNetFx_Full_x86_x64.exe
...\Steamapps\common\stronghold3\resources\redist\ vcredist_x86.exe
...\Steamapps\common\stronghold3\resources\redist\ vcredist_2008_x86.exe

Restart Windows and run the game.