In this case, there's no way to be sure what the order of events is, because there's no particular connection between drinking milk and playing computer games. The two things might even have been simultaneous. In the most literal sense, "and" just means the two things on either side of it are being asserted: "It is true that I had milk. It is also true that I played computer games."
However, most speakers have some sort of reason for saying things the way they said them. The fact that the speaker mentioned the milk suggests that they feel the milk is more important or that it came first. Most people are probably more excited about playing computer games than drinking milk, so it seems more likely that the milk came first. On the other hand, it may be that they were just mirroring something that was said to them. For example, if somebody said to me "Did you have milk or did you play computer games?" I might say "I had milk and I played computer games," even if I drank the milk afterwards.
In other situations, you can infer the order because one of the things has to be done first. For example, if I said "I opened the door and walked through it", you know that I must have opened it first, and then walked through. (Unless I'm a Gumby. Which I'm not. Even though my brain hurts.)