There is no way it's anything as advanced as MP3.
It's probably a simplistic codec that was originally designed for speech and not music, which would explain the crappy audio.
There are a bunch of specialised microcontrollers designed for toys with like a 4bit CPU, a few GPIOs, 64 bytes of ram and a big massive mask ROM (like a few hundred KB) to hold audio data. They are designed for toys were you press a button and the doll speaks a random catchphrase. One of the common chips in the era was the Winbond "PowerSpeech", which used 4-bit ADPCM at 6khz, 8khz, or 12khz
I think Tiger just took one of these MCUs, picked the biggest mask ROM available and put a single 60 second music clip on it.
The PWM described (~8 MHz of one bit PWM) ought to be capable of far better fidelity than we see in Techmoan's video or the linked audio from the blog post - it's pretty similar to (mono) Super Audio CD for example.
So that's why I end up thinking that the interesting part is probably in the chip you can't easily get at. Like maybe it's MPEG audio layer II with a PWM decoder or something.