That does look like learned behavior, rather than an actual artistic expression. Notice the care it is taking to reproduce the lines as exactly as it can, I'll bet the trainers deny the food reward if the "portrait" is not recognizable. Now, if the elephant does this using other media, like drawing in mud, or changes the lines and their order to make the same portrait, then I'll start believing it.
Elephants are pretty far up there as far as raw brain power goes. It takes a decent chunk of brain to control the manual dexterity (um, trunkal dexterity?) that they have. Elephants in the wild have been observed using logs as stools to reach branches otherwise out of reach, and using twigs to knock down fruit from further than they could reach. That'* tool using behavior, and it'* pretty indicative of higher intelligence.
There'* always that elephant that was at the Cincinnati zoo back in the 50s and 60s. He figured out that people carrying popcorn bags would feed him popcorn. But sometimes they wouldn't, so he would toss rocks at the people who didn't! After a couple people got hurt, the keepers put up a sign on his enclosure banning popcorn near it.....The elephant tore the sign down, and started throwing rocks at anyone who tried to replace it.

It'* still a neat thing to see reguardless of why they do it.