As I see this question, it all depends on how the author wants to treat the antecedent. If he/she chooses to consider it as a set of activities, then he/she can do away with "activities", but then has to change the number of the verb.
- They may play games, sports or simply sit and chat together, which is far healthier than sitting alone hunched over a screen.
On the other hand, if the antecedent is to be treated as separate activities, "activities" is necessary (and the number of the verb remains unchanged, of course).
- They may play games, sports or simply sit and chat together, activities which are far healthier than sitting alone hunched over a screen.
The reason for that would be that the identification of the antecedent is not made easily in this case; there is a missing point of view: you could substitute "pastime" for activities, and the sentence would make sense too, but you'd be looking at the things mentioned under a somewhat different light. you could even speak of time-killing activities, instead. You might then say "But why should one choose among the possible points of view available?", and there is nothing I can answer, particularly so, in the light of the possibility of treating the antecedent as a set; nevertheless, using a "rounding-up term" seems rather necessary to me.