No, but it does need to be distributed in such a way that users can replace the ffmpeg provided with the product, with their own version of ffmpeg (and of course, provide a source from which the distributed ffmpeg can be built, unless it’s already configure/make/make-install upstream. Some say even if already upstream)

But also, depending on codecs, it might be GPL; e.g. x264 itself is GPLd as are some other codecs. There are BSD licensed codecs. As ffmpeg relies on many other projects to provide codecs, it’s on a codec by codec basis - though the original configure makes it easy to disable all GPL upstrrams.