What is the name of this sort of Platform?
Welcome to ELU, 312.
Perhaps 'gallery' is the most appropriate word here, as the setting looks historical. Otherwise, I'd agree with Jan's 'balcony'.
gallery NOUN ... 2A balcony or upper floor projecting from an interior back or side wall of a hall or church, providing space for an audience or musicians. {ODO}
A gallery is usually an interior feature:
gallery 3. countable noun ... A gallery is an area high above the ground at the back or at the sides of a large room or hall. {Collins}
although not necessarily:
Gallery ... 2a : an outdoor balcony {M-W}