Does a master's research project (not a thesis) count as a "publication" for PhD applications?
If it's printed in your institution's library it is fair to say that it was published by your university. You may want to explicitly list it as a technical report in your bibliography to clarify the type of publication that it is (your audience will want to know if your publications are peer reviewed or not). 

Under the list you have here it would be an "Other" that is "Published".