Ok, I've made some headway on this problem. Looks like mod_h364 VC14 is working fine.
I can play it on Chrome 15 and IE10.
So the problem seems to be with the Firefox compatibility.
On Firefox 36 I can't play ithe html5 tag but I can play it in video.js player.
On Firefox 40 I is the same situation. So this is definitely Firefox compatibility problem which was dragging all along when it comes to MP4 format. On another hand both the Firefox 36 and 40 on my system will play webm and flv files without a problem and some MP4 files but not all.
If you remember at one point Firefox was trying convince everybody that mp3 format is a bad idea and we should use ogg

Do HTML5 players in the various browsers actually support streaming or do they need to download the entire file first?
On my system Firefox 28 and newer, Chrome 15 and newer and and IE10, all support streaming.
As far as Gregg's page speed is concerned it loads relatively fast for me in the US but different countries have different backbone links so depending where the page is hosted and where from is being viewed the speed will differ.