Yep, the video shows the elephant executing a trick it has been learned to do rather then "expressing itself" by having it freely mess around. I've withnessed some of this myself in Thailand, were they had two elephants paint something (not quite sure what it was supposed to be though :p ). The "free style" painting is much more artistic. Not really natural either since you still have to make the elephant learn how to use paint.
But if the paintings are sold for a good purpose I don't really see the harm in it. Though I'd acknowledge that the living conditions of some of these elephants might be a bit poor (stressed elephants and such) which could use some improvement. But we see these conditions improving, and let's not forget that 50 years ago the animals overhere in zoos asuch were not really threatend in a natural, responsible way either.
Though I think some animal rights activist are taking things a bit too far, one can offer animals a respectful, caring enviroment were they can live without going nuts yet learn them a few tricks for various purposes such as entertainment or labour. To truely let animals live their own, natural, lives would mean we'd need to set them all free (yes, that includes pets too) and not keep any domasticated animals at all anymore. :p That's not really an option either.