Is self-control a significant factor in chess improvement?

I would say, yes definitely, in that self-control is a subset of discipline. In my work as a psychologist, one of the first things I would do with a new client is teach them chess. In doing so, I could pinpoint causes of problems that arise in the classroom. (If a child has a self-control problem, chess will bring it to the surface.)

And then I tell them the story a bout the two monkeys. The young monkey says to the old monkey, with great excitement, "Hey the bananas are ripe, lets climb up a tree real fast, and eat a banana." The old money, with a wise sort of calmness, says, "No, let's climb up very slowly and eat them all."

When we go for the easy wins and set traps that only work if the opponent makes a mistake, whenever, for any reason, we choose not to do the best move, then we need to think like the old monkey.

I had read a blog about self-control on chess.com. I do believe that everyone has some self-control issues. I also believe that chess can help/teach people who have self-control issues, because you're staring at a chessboard for minutes/hours at a time.

I guess we mean different things when we say self control!

I mean that an individual is able to handle himself and not overreact, losing his temper in any critical situation or any situation at all, like seeing a beautiful woman and runs straight to speak on her or anything like that

What you describe as self control seems more like focusing, or lack of focus