The engagement was in P&P2, but not in the novel. In the novel, Wickham was not engaged to Miss King.

I didn't really like the addition, either, but it is a good way of dramatizing Elizabeth's reactions which the book mostly described. Perhaps it worked well for those persons who had not read the novel yet.

I also think they put it in P&P2 the way they did to show us:

(1) Wickham really did like Elizabeth and acted honourably toward her.

(2) Elizabeth was not too upset and still liked Wickham.

(3) By making it an official engagement, the gossip that Lydia shares with her sisters about Miss King leaving is more surprising.