The largest piece of evidence here is not about sport at all. It is a review that pooled 148 separate studies covering 308,849 people, following them for about seven and a half years on average, and asked a plain question: does the strength of somebody's social relationships track with whether they are still alive.
It did. People with stronger relationships were around half again as likely to be alive at follow-up. A later review by the same group, across some 3.4 million people, put numbers on the other side of it — social isolation, loneliness and living alone each showed a raised risk, of broadly similar size.
That is where the Copenhagen table becomes interesting rather than merely surprising. Its authors noticed that the activities at the top all require another person, and pointed at social interaction as a likely part of the explanation. Two independent bodies of work, pointing at the same thing from different directions.
None of this proves that joining a club extends anybody's life. It is an association, arrived at by two independent bodies of research coming from different directions — a reason to take the company you play with seriously, not a promise about it.
Observational study — it shows an association, not that the sport causes the outcome.
The half that is not exercise — Social relationships and mortality risk — a meta-analytic review. PLOS Medicine (2010) · PMID 20668659