Combine Yakisoba sauce, garlic, orange juice, and ginger in a large bowl. Season chicken with salt and pepper and place in marinade. Cover and refrigerate for 4 hours.
Preheat grill to medium and carefully cook chicken. The sugars in the marinade can burn, so keep watch on the heat to prevent flare-ups. When chicken is thoroughly cooked, remove from grill.
In a medium saucepan, combine quinoa, orange juice, water, and a pinch of salt. Over high heat, bring to a boil. Reduce to a simmer, cover and cook 15 to 20 minutes until all liquid is absorbed. Fluff with a fork.
In a nonstick pan, over high heat, add a bit of water to the pan and stir fry the vegetables in batches until just tender.
In a small saucepan, over medium-high heat, combine honey, orange juice, and kumquats. Cook until the kumquats start to become translucent. Add vinegar and cook to reduce. The sauce will not be thick.
To plate, place a scoop of quinoa on a plate and top with vegetables and chicken. Spoon the kumquat gastrique over the chicken, vegetables, and quinoa. Serve immediately.