There seems to be an ongoing trend with indie devs to go with a pseudo 16 bit art style when approaching game developing. Is there a particular reason why they choose to make this style, or is it a design choice?

Its the natural result of resource constrained development, you try to make the best of what you have.

I suppose the answer is different for each case, for me it's a design choice.

I'm making an 'old school' jRPG style game. They look and work great in the 16 bit graphic style that was state of the art when these games came out (think: Final Fantasy VI, Chrono Trigger, Legend of Mana). Honestly, 3D doesn't add a whole lot to those games (see: the DS remake of Final Fantasy IV), and I suspect vector graphics wouldn't either (though there is something to be said for pixel based movement). It also lets me use a simpler engine and focus on other parts of game development, and if I want custom artwork, there are artists who can do it well without charging me half my lung.

If I were making an action FPS, I'd make a different design style choice.

Audio, OTOH, I want as high quality as possible, particularly the background character theme and area musics.

Personally I think it's a result of many indie designers not having a f'ing clue what modern vector art is. They seem to think, "Oh, I need to do something cheap and simple since I have next to no budget, I better copy an NES game!" Sorry about the bitterness, but I detest pixel art. Though... I suppose developing for a phone might be a legit reason to use pixel art.

I'm making an 'old school' jRPG style game. They look and work great in the 16 bit graphic style

Whether an art style "works" is really dependent on the individual member of the audience, not the game genre. It's just a matter of taste. I'm not the only person I know who can't stomach playing actual SNES games any more mainly due to the graphic style. This is true of all of the major art styles - there are people who can't stand any kind of anime style, people who can't stand a western superhero style, people who can't stand an oldschool D&D style, people who can't stand 2D art at all, and people who strongly prefer 2D art to 3D art.

I'm making an 'old school' jRPG style game. They look and work great in the 16 bit graphic style

Whether an art style "works" is really dependent on the individual member of the audience, not the game genre. It's just a matter of taste. I'm not the only person I know who can't stomach playing actual SNES games any more mainly due to the graphic style. This is true of all of the major art styles - there are people who can't stand any kind of anime style, people who can't stand a western superhero style, people who can't stand an oldschool D&D style, people who can't stand 2D art at all, and people who strongly prefer 2D art to 3D art.

In regards to preference, of course you're right. I was referring more to pure functionality. All the mechanics in my game 'work' with the 16 bit style pixel art. If I want to get fancy I can parallax. In contrast, a high-speed precision FPS game simply wouldn't function under those conditions. You wouldn't have the detail required to 'see' your target, not to mention movement and other issues that would arise.

I'm sure some people won't give my game a second glance because of the art direction I'm taking. I'm counting on the niche of players that will.

Can anyone direct me to other games of a large scale(not mobile or casual) that have applied good non-pixel style art?

Limbo has an interesting "silhouette" style of graphics.

Samorost and Samorost 2 use an unusual style that makes use of a mix of vector graphics and real photos. Machinarium has a similar style.

I'm not sure how to describe the graphics in Bastion, but they're a very "artsy" style that is quite effective.

Psychonauts is stylised 3d.

The Binding of Isaac has a dark cartoonish vector-looking style.

There are loads of non-pixel styles out there to explore, although obviously personal preference plays a huge role.