I play computer games - this one is probably most natural and suitable in most situations. If can add the verb 'do' for emphasis. For example: Me: You wouldn't understand what I am talking about since you don't play computer games. You: I do play computer games. (Here you would add the verb 'do' to contrast what I have said, and to emphasize your point).

“I play computer games” is correct. “I do play computer games” is incorrect because “do” is unnecessary. You only need one verb here