None of the lighting on the vendor pages is DOT approved. However, that does not make it illegal. What makes it illegal is the various state laws. DOT or more correctly NHTSA, set's the minimum requirements for vehicle lighting including location, placement, color and brightness (lumens) and number of lights. It also sets requirements for reflective materials including standard plastic reflectors and reflective tape. Standard vehicle lighting must also have the DOT logo on the lens or cover.
While additional lighting is allowed, it must not take away from or interfere with NHTSA and state regulations. As far as LED lighting sold by vendors, it doesn't meet DOT regulations because it is an added feature not standard on the vehicle at time of manufacture.