This is what our old dog Maggie has, we think. She had this a few weeks ago and it was very alarming, she was stumbling everywhere and very ill, but she improved within 48 hours. Last week she had a relapse, and although she's doing better she looks just like the dog in the linked article, with her head at a sort of permanent tilt. It's kind of cute, really, it fits her personality. She has always been a bit aloof and somewhat confused-looking...when she was a younger dog we always referred to her as the Doubtful Guest because she bore a resemblance to this Edward Gorey character.
It's difficult watching her age, she's a good old girl.