The current server version of Confluence does not support adding people to watch a space (from that menu, at least). The Cloud version of Confluence does allow you to do this, but that feature was released only a week ago!
There is an option you could use until then, though, if you really need it.
I wrote a user macro to allow admins to be able to manage watches for other users, including adding/removing space watches. It's here:
Just save it as a user macro under some name (and set to only show to administrators), add it to a page, and then you should be able to use it without any problems
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