Would you argue that playing a card or board game is sinful? After all, someone wins, hence there is competition.
The key distinction is sport vs recreation.
Why?
Because Pius XI said we had to be careful to protect feminine reserve.
And where sport by nature excites the passions (thereby surrendering feminine reserve: think of the tennis player in the 1990’s going down to her knees after victory and ripping off her top in exuberance), recreations (eg., boardgames, hiking, fishing) do not elicit such passions, and therefore present no threat to feminine comportment or reserve.