I'm not sure I agree with the key change used based on what I can see. Can you show the next few lines as well (after bar 64)? It's possible they consider the g sharp minor chord the parallel to the tonic, which then would be B major, since they are doing E major -> F sharp major -> G sharp minor (subdominant -> dominant -> tonic parallel in B major). But I would like to see the next few bars to help me determine that.
If my hypothesis is correct the first marked chord in bar 60 (A major with an added 6) is the subdominant to E major, and I'd argue that the final two beats of the bar give you a feeling of B major 7, ie the dominant to E major, and then you have E major in bar 61 (I know an F sharp is included, but I'd view that just as the 9th added as a color), which is then the subdominant to a B major tonic, followed by F sharp - the dominant - and finally the tonic parallel (g sharp).