As group 2 in the periodic table comprises of metals, the reactivity of group 2 elements towards chlorine increases when working our way down the group 2 metals. This is compared to non-metals when the reactivity decreases working down a non-metal group such as group 7.
Metals have less electrons in their outer shell compared to non-metals and hence in reactions they give away their outermost electrons to the non-metals, as it is easier to ger rid of few electrons than many. As we work our way down group 2, each successive element has increasing number of shells and hence increased atomic radius, so the outermost electrons experience less attraction to the nucleus and can be transfered to the non-metal element more easily. The decresing attraction between electrons and nucleus is called shielding and therefore as we work down the group there is increased shielding. All of these effects contribute to increased reactivity of group 2 when going down the group.