The reason most programs require the GRE is because most of the Masters in Finance programs are offered through the math department, stats department or a colaboration of both (mix in the comp sci. dept. for fun too). So when you apply youare apply to the graduate school for letters and science not the business school. There has been a recent development though, and programs are starting to recognize the GMAT as an alternative to the GRE General Test.
In response to the GRE Subject Math test, when you apply to to these programs you might think that you are competing with MBA students. But in fact, a MAsters in Finance is highly quantitative, and most applicants dont have an econ degree, they hage engineering degrees and math degrees. In order to stand out among these people you should consider taking the GRE Subject Math Test and scoring about 850, or atleast 800 (out of 990). It should be noted that when you begin your Masters in Finance you would want to know what a PDE is, and be comfortable with computational mathematics. At the very least you are going to want to be extremly versed in calculus and be familar with some sort of programming language.