Brief Answer:
Possible but not necessarily.

Detailed Answer:
I read your question carefully and I appreciate your concern about your friend's son.

The pituitary gland produces several hormones. They are involved in many functions regarding growth, metabolism, sexual development etc and their lack may be associated with intellectual deficits. It is true that he is taking replacement therapy but such a fixed dosage as much as it tries is not perfect. Furthermore I wonder about other hormones such as thyroid hormone production which is also controlled by the pituitary. If there is a deficiency of thyroid function that may well explain the memory deficits. However I would assume the doctors have already tested that, if he's not getting any treatment means there is some function left and thyroid function was fine.
Another factor to consider is the possibility of other associated brain anomalies you might not be aware of, since this is a born anomaly there may be other brain areas affected apart from the pituitary gland.
So the answer is yes his condition may have something to do.

That being said, being possible doesn't mean it is necessarily so. Addiction to cell phone games is a very common phenomenon in today's young population, even in the absence of any hormonal issues, isn't really a distinctive feature.
As for the memory issue you mention that is hard to assess only by the fact he doesn't remember what you told him. Often when memory deficits are evaluated it is simply the case of lack of concentration leading to information not being retained not a memory issue. That is why when deficits of memory are suspected they are evaluated through neuropsychological tests which assess different aspects of cognitive function through dedicated questionnaires and tasks. I assure you that in many cases no real memory deficit turns out, only concentration issues. So such neuropsychological tests are advised before reaching to hurried conclusions.

I remain at your disposal for other questions.

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