While I agree that this certainly isn't the worst action of a CEO ever (nor this year or probably this day), I can understand the outrage a bit.
First of all, controlling your public image is a good idea, most of the time. Unless you want to go totally over the top and take it too a Donal Trump level. Hunting probably belongs in the same class as politics, religion and sexuality: Don't talk about it too much.
Second, it's hunting in Africa. Trying to look like you're the protector of a poor village there is going to bring back things like the "White Man's Burden" into the mind of people reading and watching this. Not a good idea, part deux.
Never mind that shooting elephants is a last-ditch effort. As far as I know there are lots of other ways to drive them off, maybe not as easy (and "entertaining") as just shooting them.
On the other hand, it's the GoDaddy CEO. Not exactly a brand with a good publicity anyway, and they barely need it. Enough people go there because they like to save money and/or don't know any competitors. Regarding needs for good publicity, they're probably somewhere between McDonalds and Monsanto.