I think it was very much in character for Arya. Her previous line of "that's not me" wasn't just a pre-pubescent girl unable to believe she'd ever want to marry or be in a relationship. It was about her wanting to be known for her own sake, not just as a lord's wife and the mother of his children.

On the other hand, I'd obviously like the pairing to be endgame, and Gendry looked so hurt by the rejection. Arya even looked upset too, because she knew that he really had fallen in love with her. I basically deal with it using 2 head-canons:

1. TV series head-canon - in a few years' time, Arya will sail into Storm's End and will need to spend a few days in the city while her ship is being repaired. She'll overhear a conversation at the inn where she's staying about how Lord Gendry is still unmarried. She'll go up to castle and insist upon seeing him. They'll begin to have a relationship every time she's in Westeros, with Bran legitimising every child they have.

2. Books head-canon - in the books, it's very unlikely that Gendry will be legitimised, because he has a younger half-brother who's mother was also a noble and who was actually acknowledged by Robert. I also think that Arya might become Queen of the North instead of Sansa, since Sansa is going to marry the next in line to the Vale of Arryn, which might take her out of the succession in order to keep the North independent. In that scenario, I could see Arya marrying Gendry (if they do ever reunite) because then she'd still be Queen in her own right, with him just as her consort, rather than her being the King's wife.