Without being too scientific about it, I think in trying to figure out what's happening on people would typically work down from the most likely explanation down to the least likely. On that basis, the possibility of it being something paranormal would really really REALLY be the last possible explanation (and even then rank some way behind a real dog scaling the wall, sneaking in the window, giving your DS a nip and then sneaking out again unseen).
That being said, and despite being somewhat, shall we say, sceptical about the paranormal I still get 'spooked' by things even when in the cold light of day you know you're just being daft. In answer to your original question, I looked up about dreams for own DS (22 months) a little bit back.
Somewhat surprisingly, studies have shown the newborns not only dream on their first day but actually dream more than adults in terms of the amount of time they spend in REM sleep. In fact children dream more than adults until about the age of three when REM patterns level out. Although it's hard to tell with kids under the age of three because of their lack of communication skills the same studies tend to agree that if the child can dream, they can also have nightmares and that there is correlation between dream activity and the extent of nightmares. So yes, DS is certainly old to have bad dreams.
Equally, whilst imaginative play generally takes off at around three, the beginnings of it starts much earlier. Along with this comes 'irrational' fears which can be absolutely terrifying for children even if they seem mad to us. Fear of the dark is a very obvious one but kids pick up so much from so many sources (TV, radio, photos, conversations, out and about, other kids) that virtually anything can become a fear if it's associated with something 'bad'.
In terms of play as well, I don't much about the pyschology of it, but even at 22 months I find DS having 'annoyed' conversations with certain toys and characters (e.g. "no, Pat, NO", cue flinging Postman Pat across the room after cuddling him a few minutes previously). The toddler mindset is a strange one but I guess the fact that he likes/ wants to see the dog and is also scared/ attacked by it isn't incongruous to him in the way that it would be to us.
That being said, it's clearly very distressing for DS to be this troubled by whatever it is he is imagining. I think the usual advice in this situation is to be as practical and sympathetic as possible and not to deny (what is to him) something that is very real. I guess in your place I'd remove anything I could from the shelves so there was nothing to cast shadows/ make shapes/ give the dog somewhere to hide behind. Make sure nothing anywhere else (e.g. curtains) is doing the same. Have a soft cuddly very cute dog downstairs maybe that he sees you cuddling (and maybe can cuddle too assuming he's not scared of dogs generally). At the same time, take him 'seriously' when he says he sees it/ has seen it and find some equally imaginative way to deal with it. A leash maybe, so you control it and can 'walk' it out of the room. A special anti-dog spray (perfume container filled with water?) that you spray at it to make it go away if he's being scared by it. Sure there's plenty more imaginative (um, stupid) ideas as well.
Just a few thoughts anyway.