I think your wrong purely based on the following observation:
When chlorine gas is passed through a solution of Potassium Bromide, the solution goes a reddish brown because the Bromine is liberated. Now think about your reaction. What would the chlorine actually do? The chlorine has a higher electronegativity than Iodine. What does this mean? Therefore, what happens to the reaction of
MgI2 with chlorine gas?