I think this trope is relevant:
Doing it for the ArtI remember Yoshi's Island and Chrono Trigger being rather artistic games for their licenses, and I was also surprised to see that FFXII was among the list as well; but when you consider what has been mention that explains why (Final Fantasy Encyclopedia unlocked throughout gameplay), the background, the detail put into it graphically, storyline, and history of Ivalice for their last game on the PS2. That game is indeed a work of art as their final piece for it; although FFX was also pretty decent (good start for a different approach to their game franchise, although X-2 didn't do as well.).
Another artistic game would also have to be anything made by Team Ico and the Panzer Dragoon series. Those games are beautiful, downright awesome looking, immersive, and the music is made of refined awesome. Good immersion, story background, and impact to make you care for not only the main characters, but even the NPCs is what really makes a game really artistic when done right. Even in Panzer Dragoon Orta, there's a side-quest that you get to play as one of the people in the military you regularly gun down with the dragon; turns out a great majority of their forces are children raised by the military, many of those giant beasts you fight are ancient weapons, some of them remodeled/tamed by the Empires to be weapons of fear and domination and etc., and there's so much more to be learned throughout all the episodes too.
I suppose I can also toss in Jet Set Radio Future as an artistic game as well. It also holds elements of unique gameplay, interesting backstory, nifty style (while cel-shading was still relatively a new style), and epic music that makes you feel like part of the crew. Starcon and Starcon II: The Ur-Quan Masters is also among what I would list as well. Despite the villain(s) of the story doing all sorts of bastardly things, you hate them; then after you learn enough about them and their motives, you then gotta feel a bit of pity for them, understand better, but for the good of the universe, you still have to defeat them so they don't destroy themselves in the process as well. All the races were unique, interesting, and funny, and really complex even; excellent graphics for the time, unique and sometimes dark sense of humor, and yet again, good music. This list can go on, but I hope these examples can provide some insight.
I think when a game maker wants to make a game, and not flourish their bank accounts, then they tend to lean on making works of art; most of the time, it just seems that they're just trying to keep their business running by repeating what works until it breaks, along with their funds.
EDIT:
I forgot to mention Steel Batallion. Holy crap, that game was not just a game, it was an all-out battlemech simulator which required a $200 controller to play it. I wish I owned that game, because holy crap, I wanted to seriously drive a mech (full console and everything like a simulator) since playing the Mechwarrior games. This game allowed that dream to come true. That is a work of art as well.