They offer people chances to escape from the busy and tiring work and have fun for a while, which like a recharge for exhausted people. However, if people relate their hobbies or physical activities to their work, they will easily think about the stressful work thanks to their leisure items.
These two sentences are not opposite in meaning, so the use of the word "however" is unnecessary.
Hobbies or sports differing from people's vocations can enlarge the scope of their horizon, which the related hobbies cannot accomplish. Handing some knowledge from fields not related to own major focus will offer us lots of benefits. People enrich themselves from those hobbies and physical activities; learn something new is always good for them for the future use.
These three sentences practically deliver the same idea in different ways, so that seems a bit too wordy for me.
You gave two examples of your parents and uncle and then generalized their cases for everyone by using "so", and "therefore". I think, logically, this is not the right way to draw a conclusion.
Apart from these issues, you made relevant points to back up your position and I really like your style.