I watched your video and you appear to be doing everything correct. I feel it must be a defective unit. My 620 works perfectly. In fact, I just had it learn another function yesterday and all went well. I'd try a replacement since I feel the 620 is one of the best universal remotes Sony has produced. I went through two 900's, in the past. One is still working fine but it is unable to learn the new four digit codes.

EDIT: Look at page 25, Step 4. Are you holding the device button down for three seconds? Your video appears that you are just pushing it until it lights.