Is that even possible, or are you talking about the link only?:D I've been waiting for a coin that will let you post videos on the blockchain, I don't think bitcoin can do that just yet ;P
Yes this is possible in Bitcoin. It will cost you a fortune and many people will hate you for it.
You can post a transaction with random binary code in an OP_RETURN opcode. Not a lot of code, but enough for a counter field and binary data.
You would then have to split the video in as many tiny fractions as needed. An OP_RETURN is 80 bytes - let's assume that you don't need the counter field and that you can use the entire 80 bytes. Let's assume that the video is 80 MB, or 80 million bytes (going by 1000 bytes per kilobyte).
So you'd need one million transactions to embed your 80 MB video into the blockchain.
Let's assume a transaction is USD 0.01 for the sake of argument and easy calculation. It would cost USD 10.000 to embed it.
Obviously it is not designed to do this though.