Given a huge sprite like this one.
Is it possible to order the elements (emojis in this case) in a way that the resulting PNG file size becomes significantly smaller?
Extra question. I've read that, in the filtering phase, for each scanline, the best filter is selected. So my intuition says that it is better to have an image where the height is much greater than the width. Does this make any sense?
Your intuition serves you well...
I split your image back up into its original icons as separate files. Then I made montages 2, 4, 8, 16, 32, 64, 128, 256 and 512 icons in width. For each width, I randomly shuffled the icons 10 times and averaged the resulting file size across the 10 runs to even out any differences. And, as you intuited, the sizes are smaller the narrower the montage.
Whether the software that reads the montage can manage an image with dimensions 64x118336 is another question...