It's like saying - there's a trained neural net with inputs: opacity of screen = 1 with expected output of searching target box. When tested, similar neural nets with similar training expected output of target box. Hence neural net has "theory of mind"
It'd be way more conclusive if the apes knew what was going on, and then decided to act to change the outcome.
It's not. There's a world of difference between a neural net and a chimpanzee. Chimpanzees are some our closest evolutionary relatives. They are living animals with whom we share a great deal of our DNA (98.8% seems to be an often quoted figure). Therefore, conclusions that are likely given the observation "neural net shows similar behavior to humans" are vastly different those given the observation "Chimpanzee shows similar behavior to humans".
That's like saying there is a 99.9% chance to survive the end of the year vs a 99% chance. Vastly different!
We share 99.9 % of our DNA with any other human being. Chimps are 12X more different than we are to ourselves - and how different we are!
Your use of neural nets is also something of a red herring: you would have just as good a counter-example with two passive devices giving the same output on the same inputs.