The following comments have nothing to do with why I found the chess scene out of place, after all, we must suppose that Anne Brontė knows better than I whether such a scene was realistic for the time, however...
I was surprised that Hargrave should challenge Helen to a game of chess; I would have assumed that the gender roles of the time would have made this unlikely.
But some looking around shows Wikipedia referring to the eighteenth and early nineteenth centuries as the
Romantic Era: "The game was played more for art than theory." And Wikipedia also has a few words to add on
female chess players in this time.
More entertaining are some quotes from this page about
Chess and Women. You have to laugh (or cry) at some of the back-handled compliments paid to women's skill at chess.
These quotes do highlight why I was surprised at the challenge: men obviously felt it necessary explain away why women played so well or be seen to be showing "gallantry to indulge them with a conquest occasionally". But then I suppose it is yet another way (as if it was needed) for Anne Brontė to show how little gallantry existed in the form of Hargrave.
I did find the predatory Hargrave to be a particularly interesting character, and I liked the way the Anne had him insinuate himself into Helen's life - and yet still Helen knew to reject him. I suppose that's why I disapprove of the chess scene as much as a I do, its lack of subtlety devalues Helen's foresight and strength of character.