Moving the employees from Sports to Games would be simply updating the departpent column to point to the new department. The question is what you are going to do with the dangling department sports afterwards?
For all employees working in Sports, change to Games.
update employee
set d# = 3
where d# = 5;
Count the nr of employees in department Games, and update the employee counter.
update department
set total_staff_number = (
select count(*)
from employee
where d# = 3
)
where d# = 3;