I always often bristle when I hear people use absolutes such as NEVER or ALWAYS, particularly in ALL CAPS.
I do agree with the overall sentiment. When I hear the word athlete sans any additional context, I think of sprinters, gymnasts, and basketball players. So does Google.
When it comes to the word sportsman, I might be more inclined to think of hunters and fisherman, but Google doesn't seem to be so sure. (If we Google outdoor sportsman, however, we can find those fishermen we were expecting to see.)
One obvious exception to the sportsman ≠ athlete argument I immediately thought of was Sports Illustrated's Sportsman of the Year. Wikipedia says:
Since its inception in 1954, Sports Illustrated magazine has annually presented the "Sportsman of the Year" award to "the athlete or team whose performance that year most embodies the spirit of sportsmanship and achievement."
The terms may not be equal, but there are some contexts where there is a lot of overlap. That said, the language might be evolving while SI clings to tradition. In other words, sportsman might have been more closely aligned with athlete 50 years ago than it is today, but the magazine might be reluctant to change the name of its prestigious award.
Bottom line: I think athlete might be the better word in many contexts, but, in answer to your title question:
Can we use the word “sportsman” to refer to a person who engages in sport activities?
is: Yes, that can be done.
The dictionary would back both sides of the argument, defining sportsman with some definitions that show it to be just about synonymous with athlete:
- A man who is active in sports.
- A man who engages in sports. A male athlete.
while other definitions are more aligned with the hunting, fishing, and boating aspects of the word:
- A man who engages in country sports, such as hunting or fishing.
- One who pursues the sports of the field; one who hunts, fishes, etc.
I think those participating in that discussion forum may have found an interesting distinction between the two words; however the assertion:
NEVER use sportsman to mean athlete
is not quite true, and fails to see how flexible the English language can be.