Many NES classic weren't released on the proper NES (Famicom) in Japan. Rather, they were released for a peripheral called the Famicom Disk System.
The FDS hooked up to the original Famicom and offered the ability to save games, along with a few hardware tweaks like an extra sound channel. This meant that not only did Nintendo have to put batteries into cartridges to allow for save games, many developers had to cut the music entirely.