Firefox doesn't use the Windows codec engine for decoding video content. I don't know why, I presume it's to keep a consistent experience (and possibly also because those codec packs used to be a major exploitation vector because they never received any security updates).

Firefox is open source, however, so there's no reason why a fork couldn't add that functionality. I personally wouldn't put any development effort into it myself and Mozilla don't seem interested, but for people who feel strongly about this there are always options.