Only thing i can think of is Halo CE,
You can pick up a copy of the game for £5 so no downloading.
It has both Fighting and vehicle elements to it and should run on most modern laptops.
You can setup a private server in seconds which doesn't require any pc knowledge and password it so only you and your partner can play.
You will need 2 copies of the game, 1 for each computer but as i said you can pick it up for pennies nowadays.