Shuriken don't seem to be adding in the strength bonus. They are thrown weapons (albeit with some properties of ammo). However in terms of damage, they fall on the side of being thrown weapons.
Page 141, left column, under Thrown weapons lists them and verifies that Strength Bonus applies.
Unless this has been errata'd. I'm betting it hasn't, but you never know.
Edit: Actually I'm not quite sure what is happening with this. I have a monk with a +2 Strength modifier who in (HeroLabs) is getting 1d2+1. So HeroLabs is giving him some kind of damage bonus, but not the full one. I can't follow why not.
Do you have them equipped in your off-hand? That would halve the strength modifier like any off-hand weapon.
I added shuriken to a blank character and adjusted the STR, and the damage changed with the STR mod.