Strength increases both normal (physical) damage as well as critical strike damage.
Focus increases both your mana pool and the fire damage that Emberquake does. It's very common to see Engineers with this build balancing the same amount of Focus as Strength.
Dexterity, for Engineers, helps negate fumbled attacks (Torchlight II's version of missing an attack). Two-handed weapons are slower than one-handed weapons, so fumbled attacks have a greater detrimental effect on your DPS. Execute chance has no effect on two-handed weapons.
Vitality increases your maximum health and armor (also affects your block chance if you have a shield equipped) However, the amount of hit points you recieve from Vitality is abysmal. You could put enough points into Vitality for equiping gear but overall it is best to skip this stat. Just focus on getting gear and socketables that add to hit points.