The browser viewport is a simple window with hardly any standard events. A page is rendered by pixel and treated later as a bitmap. A browser builds an hierarchy of web page controls and display elements and keeps it in memory. Whenever mouse moves across the page, the browser algorithms search through this hierarchy to identify whether these particular coordinates belong to, say, a button or a link and then change the cursor to pointer. In short, it s what a browser engine is all about. Parse HTML to an hierarchy of controls, then parse CSS and update properties of these elements then render the controls under consideration of their properties to a viewport, then process user input and when required initiate a request. Browser engine also executes JavaScript code and performs manipulation on the document structure.
Remember also that FireFox exists for Linux as well in which case it would make no sense for browser developers to work with standard windows events. Some basic initialization code is definitely platform dependent but after the window is prepared and user input is forwarded through some abstraction layer to the core, then the browser engine leads the play with no concern for the underlying operating system and its event system whatsoever.