Indoor vs outdoor lighting
This is a common question we get when people want to install electronic components from electronics supply houses into their home wiring.  They point to the UL listing on an Ohmite resistor, and they say "It's listed, see?" 

The answer is that certification of a component, is not at all the same as certification of the entire piece of equipment.  Leviton will place that same Ohmite resistor inside an appropriate cage and sell it as equipment for home wiring.  

And so it is with your toy and cord.  The tag on the cord only applies to the cord as a component.  The entire toy has a separate rating which is more restrictive. 

That said, the life-safety issues of using the toy outdoors are largely prevented if you are plugged into a circuit that is GFCI protected.  The protection can either come from a GFCI+receptacle device, or from another piece of GFCI equipment on the circuit between there and the service panel, such as a GFCI breaker, GFCI receptacle indoors, or GFCI stand-alone "deadfront".