In "King Solomon's Mines", the men seem to have an outlook on the hunting as an obsessive hobby. He writes in great details about his guns and ammunition, along with complete descriptions of the joyful experiences he feels while hunting. The men seem to come together in a sort of evil savage manner while hunting, and their all around respect for nature is disgraceful.
It is also very apparent that the book is trying to connect their hunting adventures with a strong sense of masculinity in Quatermaine. They are on treasure hunt in South Africa - a reflection of the movie Indiana Jones and the Temple of Doom. Indiana Jones played a role involving a powerful role of a masculine hero who adventures through the jungle and overcomes the death defying odds, and I believe Quatermaine is playing this exact role so far in the book.
As far as hunting back in Quatermaine's days and the sport of hunting now, it is not even comparable.
Big game hunting has since been outlawed in Africa, and the Humane society has set down strict rules and regulations for game hunting. I believe that back in the time of the story, Quatermaine did not necessarily see the entirety of his bad morals and ethics. Even if he did not consider the act of hunting game as morally wrong, he did not have anything on his shoulders making him feel guilty about breaking any laws.