Based on Juliens latest comment above with info about a trick by adding allowfullscreen webkitallowfullscreen mozallowfullscreen
to the code for the iframe, the only solution is to add the same code to the code that creates the iframe in the highslide-full.js file (or the highslide-with-html.js file - it depends of which Highslide file you’re using).
Open the Highslide js file in a text editor (not Word or similar) and find this line:
(line 1668 in highslide-full.js - line 1435 in highslide-with-html.js / both version 4.1.13, the line number might change in later versions)
this.body.innerHTML += '<iframe name="hs'+ (new Date()).getTime() +'" frameborder="0" key="'+ this.key +'" '
Change the line to this:
this.body.innerHTML += '<iframe allowfullscreen webkitallowfullscreen mozallowfullscreen name="hs'+ (new Date()).getTime() +'" frameborder="0" key="'+ this.key +'" '