To win their guerrilla insurgency, I would say they would have to forge tactical unity with other groups such as the Túpac Amaru Revolutionary Movement - which they fought against IOTL. With a united front, the “people’s war” in the countryside would probably be more successful and perhaps the Peruvian government could topple given their extremely unpopular tactics of repression like rape and torture.
I’m sure there would be political purges and killings, but what particularly would lead them into some Latin American Pol Pot style Killing Fields?
The Shining path philosophy sounded exactly like that of Paul Pot. With very similar ideologies you can expect very similar results. There are also hints and could have gone full North Korea. I saw some shining path propaganda videos a few decades ago and they looked like a Bargain Basement North Korea propaganda, it involved poor farmers in a village having a mandatory march everyday before work and praising the virtues of The Shining path.
If The Shining path came to power the body count would be at 1 to 4 million, depending on how good they were and shutting down Escape Routes.
The body count could get higher if the government lost touch with reality and created a famine trying to collectivize Farms
I've talked to several peruvians about this and they said if The Shining path had to come to power Millions would have died.