That list, I think, is from before we actually had a level editor for JJ1, so it's kind of outdated. JJ1 tile animations are all palette swaps, as cooba says, but just saying they're hardcoded simplifies the issue a little. In the (Level) Properties window in J1E, you'll see an option called Background Effect. This controls various things related to the palette, including, although this isn't actually documented anywhere, which sequences of colors in the palette are animated. 112-115, 116-123, and 124-126 are always(?) animated, whereas other sequences are only animated for certain settings of Background Effect. For instance, Battleships has a setting that animates 128-191 and 192-223, and Fanolint has a setting that animates 192-223 and treats 128-191 as a tiled parallax background of the type seen also in Tubelectric, Crysilis, and Ceramicus. Documentation for Background Effect is limited and sometimes inconsistent, so... play around.

(All animations that are not simple palette swaps, like the spikes in Exoticus, are animated sprites.)