A Vindication of the Rights of Woman is not a satire. It is a straightforward exposition of ideas which present-day scholars would usually regard as "pre-feminist" or "proto-feminist." In some ways it's analogous to Thomas Paine's Rights of Man, which had been published the previous year (1791). Both books are attacks on the conservative and reactionary forces of the time, and both express views which, while they were controversial in the late eighteenth century, are today generally accepted throughout most of the world. But neither Paine nor Wollstonecraft did this in a way I would label satiric.
If Wollstonecraft had taken an existing book that demeaned women, and then parodied it—writing similar thoughts in an ironic, exaggerated way to make them look ridiculous—this would have been an example of satire. Swift's A Modest Proposal, for instance, ironically presents an idea that is an exaggerated (and barbaric) version of the very thing Swift abhors and intends to criticize. Wollstonecraft does not use this method to get her ideas across. Instead, she writes without irony and without assuming a persona that is the opposite of herself (as Swift does). She writes passionately in favor of progressive ideas, but not satirically.