The person you replied to is also incorrectly representing his side, but basically you need to also understand what 'private property' is refering to.

The vast majority of communists define it as it's represented in the original meme since they approach communism as an economic strategy and not a social one. Private property as defined by captialist governments only refers to the things listed above like farm, office building, ie. anything that generates capital.

All other communists who don't agree on this definition of private property are also disagreeing with Marx himself as this is his set standard.