Immigration officer stamped my parents' passports for 2 months of stay but the official and online I94 record shows as 6 months. The exit stamp on the passport says Oct 1, 2019 while the online I94 record says admit until Jan 27th, 2020. Their ticketed return date is Oct 7, 2019.
What should I follow? My parents are visiting the USA and are on a vacation.
There's clearly an error here and your parents need to resolve it or they risk being treated as overstayers if they don't leave by 1st October.
They can take their passports to the nearest CBP point of entry or Deferred Inspection site and get the records corrected. I would expect that a reasonable officer would extend the passport date beyond 7th October, but there is a possibility that they'll stick to the 1st October date and update the online records to match.
Find a Port of Entry
List of Deferred Inspection sites