Thanks to Paddy Johnson for including some of my GIF-making and -collecting efforts from the 2000s in part one of her animated GIF art history on Artnet.
What the Walker tweeted is actually an mp4 video file, because Twitter, like Facebook, won't let you post a GIF without converting it to its preferred format. I can't complain about that, having shown the same GIF as an mpeg-2 (DVD) file, in a gallery setting.
Johnson mentions OptiDisc as an early-ish "GIF shown in gallery" example. The version above was, in fact, created because I'd been invited, in 2005, to submit one of my web animations to a show and had to do some thinking about how to present it in "real space." The earliest version of OptiDisc was a smaller one posted in Feb. 2004 (so it's ten years old!).
I posted a series of DVD-format-friendly "sketches," still in GIF form and prior to any conversion, got some comments (back when my blog had comments), and then I picked "Number 5A" -- which was the one that got the most internet circulation and I still consider the definitive version.
OptiDisc's first gallery appearance was a 2005 group show curated by Christine Vassalo and Matthew Fisher under the name MatCH-Art, which showed at SICA (Shore Institute for the Contemporary Arts) in Long Branch, NJ and then traveled to one other venue. At SICA the animation was projected in a theatre-like space; for the second leg of the exhibition run I asked that it be shown on a small-ish CRT screen (I think they used an LCD monitor).
For the show at And/Or Gallery in 2006, mentioned by Johnson in her article, Paul Slocum showed it on a vintage CRT computer monitor. At artMoving Projects, later that year, it was shown projected.
In a 2007 show in Perth, Scotland, the GIF file was converted to a Quicktime (.mov) file, a cousin of the mp4 above.
OptiDisc's life as a GIF has mainly been on the internet, where it has been shared around (hotlinked or otherwise), with and without regard to context.