There is no mention anywhere of any other way of using it except on the download page.
The first time I went there I didn't click on the download button because I didn't want a browser-based app.
Instead of just telling someone they're wrong, explain why. How is Zotero not a browser-based application, and how does it do everything OP described?
Zotero retrieves PDF metadata using a Google Scholar lookup, a method that Mendeley later adopted: http://www.zotero.org/support/retrieve_pdf_metadata
This process can also be applied to a watch folder using the third-party add-on ZotFile (Zotero supports extensions): http://www.columbia.edu/~jpl2136/zotfile.html
Zotero has always allowed all kinds of searching of metadata and content: http://www.zotero.org/support/searching
Zotero also includes notes (and these notes can be pulled from PDF annotations using ZotFile): http://www.zotero.org/support/notes