There is also a new G+ App on iPhone (it was even released before the Android version). But doesn't the same objections apply to that like on Facebook or Dropbox? Privacy concerns, most people aren't on G+ and are locked out or limited disk space? Of course he could just send Video to Youtube or Vimeo but then there are other objections like that these are separated places from photos. In the past flickr was here king but now I also see many Photobucket.com links (if one wants to avoid Facebook). Their website says they also do video and have "unlimited space" but I don't know what other restrictions apply for a free (or paid) account. But as the OP I would look into it.
What the OP really wants is his automagical "Photostream" to be shareable and to also handle videos. The first seems logical. I think this is a large customer request and it would be the next logical step for Apple to do with Photostream. But I would bet against on Apple including videos. HD vids are just to large, would gobble up tons of space in the iCloud and burn through battery life/traffic with an automatic upload.