Whisk together wine and cornstarch in a small pot to form a smooth paste.
Add cranberry sauce, butter and cinnamon. Cook over medium-low heat, stirring until mixture comes to a boil. Cook, stirring an additional 3 minutes. Remove from heat. Pour half the sauce, about ¾ cup (175 mL) into a pitcher to serve with grilled chicken and set aside.
Put the drumsticks in a medium bowl or plastic bag. Drizzle with the remaining sauce. Toss to coat.
Preheat grill over medium heat. Remove chicken drumsticks from marinade and place on upper rack. Cover and grill, turning once, until fully cooked and browned - about 15 minutes per side or until a thermometer inserted into the chicken reads 165°F (74°C). Brush each side a few times with the marinade or until it is all used up.
Serve with the reserved cranberry barbecue sauce.
If you want a gluten-free version make sure you use a gluten-free cranberry sauce and cornstarch.
The cranberry glaze has a subtle cinnamon flavour and you can increase this up to ½ tsp (2.5 mL) for a stronger flavour.