Many thanks for providing the link to your gallery.
The problem is that you've set expandInNewPage="TRUE" (in conjunction with useFullscreenExpand="TRUE").
The gallery can be expanded either on top of its own embedding page (with useFullscreenExpand="TRUE" or useFullscreenExpand="TRUE") or on a new page of its own (by setting expandInNewPage="TRUE").
The gallery can be displayed using the Fullscreen API only when it is expanded on its own embedding page. (The Fullscreen API cannot be invoked when the gallery is expanded on a new page.)
Therefore, when expandInNewPage="TRUE", useFullscreenExpand is redundant and it not used.
Just set expandInNewPage="AUTO" (or remove the entry completely as the default value for this option is AUTO) and this should resolve your problem.
Incidentally, when expandInNewPage="TRUE" (and useFullscreenExpand is not used), the Expand Button will be displayed on the Button Bar only if the gallery is embedded at less that 100% x 100%.
Please let me know how you get on. Thank you.
[Posts split from Feature Request forum to new thread.]