I honestly had no idea what the game mode involved, but I simply played against an easy AI, I had Captain Cutter.
I just built my base up really fast, two supply pads, then a reactor, and kept building up my base. I won the game without even trying in what felt like less than 5 minutes!
I think against an easy AI you can do just about anything useful and you'll win quickly as the AI doesn't do much.
EDIT: Thanks to Dibbs93, here's what Tug of War is about:
"""taken from halo wikia 'Tug of War is a game mode in Halo Wars that is won by having a stronger army than your opponent. Defeating enemies is essential, but success is determined by a combination of the army, buildings, and resources left standing in the end. It can be obtained as a game mode by downloading it from Xbox Live.'
so basically you need to make sure your army strength is always higher than your opponents"""