I skipped the ginger and used regular white vinegar like a comment mentioned, and this turned out just fine. The sauce you make out of the juice the chicken cooks in is how you get the traditional teriyaki flavor and feel. If you skip this step it's just vaguely soy sauce flavored chicken.
Also, the recipe calls for shredding, but instead I cooked the chicken until just done enough and cut the thighs in to strips like you would regular teriyaki. So in the end I had proper teriyaki chicken strips with a homemade teriyaki sauce, and made rice to go with it.
