No it isn't. Searching for something isn't a "physical" challenge. It's also not a sport if I drop my contact lens on the kitchen floor.
Bowling is a sport. Fishing is a lot more strategy than physical skill, so I would say it is not a sport. I haven't hunted so I don't know where it falls. Hunting and archery are superficially similar, and archery is an olympic sport, so maybe hunting is too.
Fishing is also a sport, AKA "sportfishing", pulling in a big marlin or tuna or another sport fish can be an exhausting challenge. Now the question can be asked: do these "sports" require athleticism? That is a physical activity requiring forceful exertion or intense energy. Considering the degree of forceful exertion and intense energy, golf does not ran very high in the athletic sports.
high athleticism: (high intensity, near continuous exertion)
basketball, soccer, hockey, football, tennis, boxing, track and field, swimming
low to moderate athleticism:
baseball, hunting, golf, sport fishing, race car driving
For these reasons, I have never considered baseball players or golfers as particularly strong athletes, as a rule. There are exceptions to every rule, some great athletes do play baseball, but its not a requirement to be a baseball player, the same with golf. The greatest athletic pursuits are in the first group.