Your variation is a king's gambit declined after white plays f4.
I don't understand Bxf3 which is not forced, black usually waits white "loses" tempo with h3, so i prefer castle for black at this point, this is what Marin recommends in his excellent "Beating the open games".
About 9.Qg3, indeed this is a mistake.
Not only because of Nh5, but even with Nxa1, black secures a clear plus.
Lane sometimes has "holes" in his analysis...
I remember this one in his "winning with the closed sicilian" :
I am currently trying to learn the Vienna Opening (1.e4 e5 2.Nc3) in favour of the Ruy Lopez as it suits me better. To do this, I bought the Gary Lane book on the Vienna, titled "vienna game", which is a good guide to the Vienna to start off with. Most of his analyses are fairly objective, but there is one particular line which concerns me (having run it through Stockfish 7):