So this is on the internet now.
Thanks again, Japan. I have been watching this video several times a day, and after such exposure, I could not help but begin to think (also thanks to the prodding of others) how this combination of behaviors could come to pass.
At its core, this is a straight-forward example of imprinting. It helps to look at the original video source, which is here. If the comments are to be believed (and I know I am asking a lot for anyone, anywhere, ever, to believe youtube comments), then the pig and monkey were without mothers, and imprinted on each other. Part of this is very reasonable, and quite obvious. The monkey is clearly treating the pig like its mother. I'm not sure about the pig, as I am not much of an armchair swine ethologist.
There are a few oddities about this video, which I intend to discuss. The story probably is not so clear as "akeminxx" would lead us to believe.
Returning to the pig for a moment, I don't know how I feel saying that the pig is imprinted with the baby as its mother. I also don't even know how old the pig is. Imprinting on adults is astronomically difficult in most animals, though. A telling moment in the video comes when the monkey falls off, and the pig bolts. From this, I would guess that the pig and the monkey were put together at some prior date, and the monkey imprinted on the pig. The pig is effectively domesticated, and when placed in such close quarters with the monkey at all hours, there really wasn't much to do but submit. Pigs are smart creatures, too.
And how about that monkey? Like I said, the monkey is clearly treating the pig like as mother. I'm not experienced enough to identify the species from the infant's appearance alone, but if I had to make an educated guess, I'd say this is a Japanese Macaque, seeing as they are popular critters... and this is in Japan.
These monkeys (as do baboons) ride their mothers on the belly, usually, but as they grow older, they will often ride on-top, in a very similar hold as they would on the belly. But they cling to their mother, and generally their mother only. I do not think a screaming fit like that put on display by this baby monkey would ensue unless the animal was separated from its "mother." So there you go: pig-mama it is.
The backwards part is very strange, though. In the baboons, one would occasionally see very young infants climb aboard their mother's bellies backwards, but this behavior was quickly rectified by the mother before she started to carry the baby anywhere. I've not yet thought of a good reason for why this baby monkey would ride backward. It might be that the animal began riding backward by chance, or some small reason, and since the pig was unable to adjust this behavior like a monkey mother, the backwards behavior stuck. Maybe there's even a semi-legitimate reason for the monkey to hold on backwards, perhaps the position affords a better hold on the pig's flanks. I would think that at this age, the monkey would much prefer to look forward than get a slightly better handhold on some tufts of pig hair, but hey, imprinting is a powerful and strange thing. There are just too many thing I don't know and cannot infer from watching two minutes of youtube.