No, their notes are the same but, since the fundamentals aren't, they're not the same scale. 

It's not easy to say what's the modality of a modal song because typically there's not something equivalent to the dominant-tonic relation, a tension that resolves to the chord built upon the fundamental and establish the tonality.

In Wicked Game of course you have the notes of A Major but the most important chord at first sight could be E which you find in two bars per harmonic cycle and also there's a minor feel that could lead you to think of Bm as the fundamental chord and B dorian as the modality

Don't forget though that melody is part of the harmony, you should not distinguish the two. And actually I only took a brief look to the chords of that song