I have multiple projectors, and honestly from 12-15ft away, 1680x1050 looks pretty dang good when it's covering a 110" high-contrast screen. Now, for gaming, be it Xbox360 or PS3 or Wii or PC, having a true 1920x1080 (or better-yet, 1920x1200) resolution makes much more of a difference to my eyes.
I used to have 3x 1200p LED-DLP projectors set up in "portrait Nvidia Surround", because NO BEZELS(!!!) plus 3 110" screens perfectly aligned equals WIN (used slightly-curved projector screens for the two side screens to make a 168-degree image without distortion!), especially for racing games, flight sims(although not my thing), and very immersive FPS's.
That's a 5'-tall display that's a little over 23' wide! Paired with my home theater's 11.3ch surround sound** it makes BF3 feel TOO REAL. Unfortunately the setup is down as I am re-doing some of the room-within-a-room construction (replacing 6" rubber matting with 10" 28-layer honey-combed variable-density sound absorbing rubber matting; 31dB reduction for the old stuff, 52dB for the new stuff! Combined with the other treatments, insulation, etc, and the home theater/studio is inaudible with both doors shut until around 106-111dB at which point the Bass can be felt as it's actually vibrating the foundation at that point!! That's with 18" between the floor of the RwaR and the actual concrete basement foundation floor!).
For the money, these projectors would be fantastic for taking to friends' houses for movies or even video games, watching films outdoors (having neighbors over to watch a movie on the side of a house), or whatever else you can think of! I have a few small projectors that I use to project images for painting walls (patterns that I create in Photoshop, I can simply project onto the wall and trace over with a brush). VERY VERSATILE!!!!!
**(DefTech BiPolar Towers and Studio Monitors, KEF Radiant Speakers, 1x Pioneer Dual-12" Subwoofer w integrated 3000W amp placed as far as possible away from seating, and 2x Pioneer 10" single-sub 850W Subs placed within 5' of seating) sucking power through an array of McIntosh amplifiers (3x 3x450W, 3x 6x200W, 2x 3x600W, 3x 1x1800W/2x900W/3x450W, 2x 4x300W) for a total of 19,050 Watts RMS + 3000W RMS (from Pioneer integrated Class-D amp). Needless to say, the entire room-within-a-room is still more heavily soundproofed than many recording studios I've worked in.... (also, there's a total of 4 speaker setups: 11.3ch film/game, 7.2ch Film/TV, 5.1ch DVD-Audio, and 6.4ch Studio Monitor setup for editing/mixing consisting of 2 channels with 3 3-way monitors per channel each one only about 50% larger than a regular bookshelf speaker but capable of 550W RMS thanks to Carbon-Fiber and Kevlar cones and 6-total crossovers inside each unit, [2 are 0.625"/2.75"/4.25", 2 are 0.5"/2.5"/3.75", and the last 2 are 0.75"/3.25"/5.125"; reason is that the setup is 99.9998% flat up to 29Khz, perfect for recording and editing/mixing] all Bi-Amped complemented by 2x 8in @ 850W RMS/ea + 1x 10in @ 1100W RMS + 1x 12in @ 1800W RMS subwoofers; speakers Bi-Amped with 12GA hex-shielded C110 99.98%-pure-Copper wire and Subs with 8GA hex-shielded C110 99.88%-pure-Copper wire).