Having the species listed as a game animal is not equal to an extermination order. Like many other states, wolves will be hunted on a quota system, probably by county. The quotas will be based on observed wolf activity and possibly based on livestock predation reports.
There will probably be a lottery to draw a tag, and drawing a tag does not mean that you will get a wolf. Having been predator hunting for a while, I know how hard it is to hunt these animals. Particularly after their first brush with hunters. Predators very quickly adapt to hunting pressure and in the case of wolves, it means 2 things: 1) Fear of humans, which they loose when they experience no danger near humans over extended periods 2) Change of habits from diurnal to nocturnal once they figure out that they do not get hunted at night.
For these reasons alone, a hunt makes sense. We do not want these predators moving fearlessly through our subdivisions or anywhere close to people. Yet this is the natural result of town and city ordinances that prohibit shooting dangerous predators near homes. A few months of activity on a sheep farm reduced coyote activity to a level substantially lower than what I have in my sub division, where they come to within 8 feet of my doors. But if I shoot one in my yard, I might get arrested. This is nothing but liberal Sierra club inspired BS. Instead we should pay government approved agents many thousands of $ per kill to hunt down the offending animals ? Of which not 1 dime goes to any legitimate conservation activity, which is exactly the opposite of what happens when the hunt is managed by the DNR.