Is a Master's thesis considered 'published'?
To what extent are these 'available online' Master's theses considered to be published?


In academia, published typically means included in conference proceedings or a journal by a publisher in some format (typically a printed book) that has an ISBN. A thesis is not published, under that definition. Nonetheless, an unpublished thesis needn't be private, e.g., it may appear online and it may be available in university library.


  what is to prevent another academic taking [someone's Master's thesis] and publishing them as their own? Is that considered 'fair game' in academia?


Such behaviour isn't prevented, but it would destroy a career, so it is uncommon.


  to what extent a Master's thesis posted online is considered to be 'published' and how it is perceived in Academia if someone was to 'plagiarize' a Master's thesis.


Such a thesis isn't published, but that's not the main issue: Academic fraud is intolerable and fraudsters will suffer severe consequences.


  how much of this (if any) should I mention in my applications for PhD programs?


I don't see any reason to mention any of it. Do you? (Perhaps add a comment if you do.)