This is the definition you keep quoting
"a person who is trained or skilled in exercises, sports, or games requiring physical strength, agility, or stamina"
Where in there does it say that the exercises requiring physical strength, agility or stamina have to be exhibited in a competition? Bodybuilders are in fact skilled in exercises that requires physical strength and stamina, so by your own definition, that would make them athletes.
So, based on your judgement, would you say fitness competitors are athletes? They are judged partly on a routine that requires skill, strength and stamina and partly on how they look on stage.
Personally, I don't think anyone can make this judgement unless you've personally been through a contest prep and gotten on stage yourself.....after you do a contest prep and compete, then come back and let us know your opinion.