Yes, but they have special formats (ETC, PVRTC, ASTC etc.) so GPU can use them directly, and the compression is lossy. e.g. PNG would not work in this situation

Yes, but they have special formats (ETC, PVRTC, ASTC etc.) so GPU can use them directly, and the compression is lossy. e.g. PNG would not work in this situation because GPU cannot decode PNG textures fast enough.