An 8 bit adder is too small and allows such 'hack'. He should try training a 32 or 64 bit adder, decrease the weights accuracy to bfloat16, introduce dropout regularization (or other kind of noise) to get more 'interesting' results.
Addendum: another interesting variation to try is a small transformer network, and feeding the bits sequentially as symbols. This kind of architecture could compute bignum-sized integers.