Yes, it makes sense to go to the supermarket for food, that we we avoid all contact with the mess, blood and suffering.
And yes, those who shoot game birds are doing it for sport. Pheasants aren't native to this country and are bred specifically for the gun - hosting driven pheasant shoots can be extremely lucrative - and the normal arrangement is that the gun (shooter) gets to take away one brace of birds, the rest are usually left to rot, although they are often given away to anyone who wants them, so not all are wasted.
I don't have any problem with shooting, it's a very humane method of dealing with pest species, but when I do it it's through necessity, I take no pleasure from it - I get my shooting pleasure from shooting hard to hit, fast moving artificial targets - clay pigeons.