The Moon won't appear to rotate because this is only covering a very short arc of its total orbit. Despite appearances here, the Moon is a long way away. The Earth's diameter is about 13 mega-metres, but the Moon is about 400 mega-metres away. So here the Moon is moving through a tiny proportion of its orbit.

So just as when you look at a very small section of a circle it appears more-or-less to be a straight line, so when the Moon moves through a tiny portion of its orbit it doesn't appear to rotate.

The clouds are moving. But you have to remember HUGE cloud formations move fairly slowly. Consider this shot is only about four hours. If you don't believe me, look at the clouds about 1/3 of the way down, over Mongolia I believe, they finish up near the center... As they move across the screen they get thinner. As far as the moon rotating, it takes about 28 days for it to rotate, this was 4 hours. So it will rotate about 2 degrees?

The clouds absolutely are moving.

Clouds don't move very much on a planetary scale over a single day: http://himawari8-dl.nict.go.jp/himawari8/movie/720/coastline...

The Earth's rotation in the original gif makes it more difficult to see the cloud movement, but it's certainly present.

Surface points on the equator rotate at about 1000 mph, while, relative to the surface, clouds move at a few percent of that; at a global scale, the clouds aren't going to move that much over the course of three and a half hours.

The moon is tidally locked to the earth and thus only rotates at about one revolution per month (about 27.3 days relative to the stars and about 29.5 days relative to the sun and to the DSCOVR satellite at the Earth-Sun L1 point which took these pictures);

Again, rotation that slow isn't going to be obvious in a time lapse covering only three and a half hours (if I'm doing the math correctly I'd expect under 2 degrees of rotation during the period covered by this timelapse)

How come the moon does not rotate?