Mxnet deepdog (hot dog not hot dog) example - how does the network know it is classifying a hotdog
You are on the right track. But you would have to realize that 713 is only, effectively, being used as an index lookup to get the weights just for that class and "seed" your new model. From there, model becomes a binary classification model where 0 is nothotdog and 1 is hotdog. Once the weights are picked up, 713 shouldn't be found anywhere else in your model. 

So the output, initially, is going to be something [0.493, 0.507], each corresponding to the probability that the image belongs to one of the two classes. From there, the call with argmax() is looking for which probability is highest, according to the binary selection. So it would pick 0.507 and call it a hotdog since that's corresponds to the binary value of 1. 

If you want to verify me on all this, go to your output code and do something like print(out.asnumpy()) and you'll see what I mean.