Instead it should have a "Slide show" menu item as the desktop version has.
Samuel Mehrbrodt committed a patch related to this issue.
It has been pushed to "master":
tdf#121457 Move "Fullscreen Presentation" to "Slideshow" menu
I agree with the idea of bringing the UI of the desktop and online versions closer together in general, with some exceptions considering the different requirements towards an online product. I'd say this case is also among the exceptions, as the extra menu only has a single entry, and the Slide menu doesn't have more than a few, either (compared to the two dozens or so in desktop), and I'm assuming there's no such problem that Slide Show would be out of place in the Slide menu. Or was it the case that users didn't find the menu entry in its original place perhaps?
I don't have any specific reports about users not finding the entry.
My opinion is that it's better to have it in a separate menu even if it contains only a single entry to make things clear and obvious.
What does UX think about this?
Consistency over modules and platforms is desirable. But I don't see an issue with this particular menu item and would keep it under Slide.