@I don't get it
HTML5 can do anything HTML4 can, including the markup for Flash. What this article refers to is the native <video> tag in HTML5 which is intended to create a single, standard markup for video. While embedding video for a particular player means unique markup for that player, not to mention complications such as, for Flash, the need for different tags for IE and Mozilla (<embed> and <object> ; I forget which goes with which), the native <video> tag is much simpler, universal and unambiguous.
The codec dispute is over what codec the content specified in a <video> tag should use. Originally the choice was the open-source Theora, which is believed to have no patent issues. Apple raised holy hell about it and managed to strong-arm the W3C into removing the codec specification entirely, leaving the choice of codec to the coders of each video; thus, some videos will play on some systems and not others, depending on which codecs are installed on that particular computer.
H.264 is considered the best performer (by a fairly slim margin), but is full of patent encumbrances (which enrich Apple and Microsoft--surprise!). That is very properly unacceptable to open-source Mozilla, which stands by the core principle of the Internet's design that says making use of Internet-standard protocols will be free and open; there will be no associated costs, directly, or as in this case, indirectly.
Any time you view a video using the <video> tag that is encoded with H.264, you are using a proprietary codec. To have that codec on your system you have to have installed a player that includes it, and they are not free, as you'd expect in the case of anything that uses patented technology. (And I'm pretty sure there's no way to get one for Linux, at least a legit one.) Also, In any case, if it's proprietary, it can be charged for, if not now, then someday, and if you have to have it to watch video that does not involve a third-party app (like Flash or Silverlight), you are paying to use <video>, an Internet standard. and that's just plain wrong.