Please could provide some information about your operating system and the source of your game (disk, Origin etc). It would help to see your error log too.
See How to Report Issues for instructions.
I'm currently running Windows 10 on my PC
PC spec:
I5-4460
GTX 1070ti
8gb DDR3 Ram
240GB SSD (origin and RA3 saved here)
1TB HDD
The exact same problem exists when running RA3 under origin.
I've tried running the game hooked and unhooked, with Origin opened or closed.
----- C&C:Online Launcher Start -----
Game: Red Alert 3
Red Alert 3 Install Path: C:\Origin\Red Alert 3\
Started game with: "RA3.exe "
Caught CREATE_PROCESS_DEBUG_EVENT from Red Alert 3. Detaching...
ERROR: game.dat process not found.