According to caniuse.com, Chrome has supported dialog since 2014. It also says that Firefox does support it, but only if you enable dom.dialog_element.enabled in about:config.
The MDN page for the dialog element does not list any such notes, nor does it contain an explanation for why it's disabled: https://developer.mozilla.org/en-US/docs/Web/HTML/Element/dialog
Why does Firefox have the dialog element disabled by default after 5 years of Chrome having it? Does Mozilla want to discourage its use for some reason?