My DS, now 12, was like that. I am very introverted so it drove me crazy.
In Kindergarten apparently the teacher finally just told him that he didn't have to say everything he thought, that some thoughts could just stay in his brain. That helped a lot.
When he was a little older, I finally thought to explain to him how he was extroverted and I was introverted, so talking to others was really relaxing for him, but having to listen all the time was really tiring for me. He was genuinely surprised to hear that I enjoyed being quiet, since it was so much work for him. Talking about it also made me more sympathetic to him. Quiet is like air for me; talking is like air for him. We are just different.
Now he's a preteen so usually I am overjoyed when he wants to talk, but there are times when it's about a video game or something and it's hard.
And, yes, letting him do screens helped. It also was great when he got to the age where he started skyping and texting with friends, because then there was someone else for him to talk to.