Hi,
I do see the problem. I think it may be related to the theme. Some themes lack a wp_footer() call, and this prevents the map templates from loading:
https://codex.wordpress.org/Function_Reference/wp_footer
You can test if this is the problem by switching (for a moment) to the standard twenty-seventeen theme. If you now see the list, you can update your theme with the missing wp_footer() call.
If you don’t see the list, try also deactivating ALL other plugins – sometimes other plugins can cause a conflict with MapPress.