There are some keyboard shortcuts but you cant play without a mouse as far as I know, I copied this from detailed how to play instructions.

View - 'V' key + left mouse button + mouse move

Zoom - mouse wheel, middle button + up/down, zoom buttons, numpad +/-

Spin - 'S' key + left mouse button + mouse move

Fine Aim - CTRL + left mouse button + mouse move

Aim - Left mouse button + mouse move

Shoot - Right mouse button + mouse move or space + mouse move

Elevate - 'E' key + mouse up/down

Move - 'M' key + left mouse button + mouse move

Pan - 'SHIFT' key + mouse move, or arrow keys ←→

The way i see it

if you do not have a proper mouse for your laptop/computer you cant really enjoy the games that well