If you are having employee engagement problems, you should first seek to investigate and solve that problem. Playing games and having contests will not solve it. I would also add that contests could well be the worst thing you do as it sets employee against employee and creates animosity between those with skills in the area of the contests and those who do not have the skills. There will also be employees who do not want to engage in such activities. You could end up creating even bigger problems.
As a former employee who hated this sort of nonsense, I speak from experience. It never worked in any organization I worked for when tried.