Futuro Futuro Kitchen Range Hoods It is most likely vented, with a duct either going straight through the wall if the hood's design allows it (very few do), or making a sharp 90-degree turn inside/above the shelf (usually concealed by a cover or soffit, and in this case further obscured by the clock and decorations). It's a tight fit but it's doable.
It would not make sense to have a ductless/recirculating hood in what looks like a high-end renovation (based on the materials and the range).