You really don't need an alpha channel for some tiny lineart thing such as the article's example. A single color would even be perfectly sufficient to make an attractive 'dancing bars' animation to indicate "sound is happening." That's my point. Some overpaid "UX designer" decided something wildly complex was needed here, and they're wrong.

In the broader sense, especially in the 'flat design' era where we don't use gradients or complex backgrounds anywhere, a 256-color GIF with its 1-bit alpha (plain transparency) will work perfectly fine to do an animated flat non-3d, non-photorealistic icon that wiggles or whatever, on a background that is almost certainly a plain flat color, and not complex enough to need 16 million shades of transparency.