I actually meant to remove autoplay from the code before posting here. The reason I had the autoplay attribute in there was because on one website it was suggested as a fix for the video not playing in IE9. But it didn't help in this case, so I meant to remove it.
It's better not to have it there, in my opinion. I often suffer what poes described—opening a few tabs and suddenly thee are multiple sounds screeching at me because some videos in those tabs started to play. When someone visits your page, you don't know that they want to watch the video (or even download it—they may be on a mobile). You really should leave the choice up to them.