I got the same results you did. A video played in SeaMonkey but when I expanded to Full Screen, I just got a gray box with a message about transferring data at the bottom of the screen.But the full screen never played.
In Firefox it worked fine in full screen. In Opera it wouldn't play at all and I got a message that my browser was not supported.
So my guess is that when the site sees "SeaMonkey," it gets confused. At least it plays. My version of Opera is using Flash 7, so maybe it would work if I have Flash 8 or later, or maybe it wouldn't when it saw "Opera." I don't use Opera 9.5 that's included with VL 5.9 because Opera 9.5 beta changes the format of e-mail for the M3 e-mail client that's part of Opera and the mail files become incompatible with versions of Opera earlier than 9.5. I don't want to put Opera 9.5 on all my computers in both Linux and Windows, so I use Opera 9.25. Flash 9 won't work with Opera 9.25, so I use Flash 7 in that.