Puree the tomato, chile and 1 cup watermelon in a blender. Add the vinegar and olive oil and pulse. Add the red onion, cucumber and dill, season with salt and pepper and puree until smooth. Chill at least 30 minutes. Loosen with a few tablespoons water, if needed.
Pour the gazpacho into chilled cups or bowls; top with dill, the feta and the remaining watermelon.