The default interpretation of consecutive 'eventive' clauses (clauses which express an action or event rather than a state) is that the events occur in the order they are specified. Since had in this use ( = "consumed") is eventive, we assume that you drank your milk first, and then played computer games.
However, it is also possible that the two events are simultaneous: it may be that you poured a glass of milk and sipped it slowly while you were playing.
In many cases it doesn't matter which sequence occurred. If it does matter, then you will have to say more to make clear which you mean:
I had milk and then played computer games.
I had milk while I played computer games.
You can also use before and after to signify order:
I had milk before I played computer games.
I had milk after I played computer games.