So, the font selection works on Chrome, but I can't download the png file. I can only copy to clipboard, and then paste into photoshop, but this way I have a black background instead of transparent background.
EUREKA ! I know where the firefox issue comes from. It's not a bug, and in fact it allows me to generate the text effect using any font installed on my computer, OR to choose from the fonts in the Font panel of the Text Effects app. This comes from the "Language and Appearance" settings in Firefox under "Fonts" > "Advanced settings", if he checkbox "Allow pages to choose their own fonts" isn't checked then the font selection in the Text Effect app is useless and the rendering will be done using the font setted in Firefox, hence allowing to render in any font installed in the OS. If the checkbox is checked, then the rendering will use the font selected in the Text Effects app.