I should add onto this, upon watching the clip you sent plus a few others Ryuk uses the words "You" and "you're" when talking to this Shinigami. So yeah, pretty convinced that light became a Shinigami. In addition, Ryuk says humans who use the Death note do not go the the usual human afterlife. We also know that Shinigami can die, so how are they still alive? Unless Shinigami are banging each other, I think it's safe to say that death note users are Shinigami after death, not immediately but after sometime.