I am pretty sure they mean the revolts from right at the start of the PRC. Wikipedia is a hostile source and I don't endorse it, but it explains well enough that the Land Reform Movement started before the end of the Civil War and mostly ended by 1953. Because the CPC/PLA only had so much manpower and China is huge, they had very little direct involvement, and instead just said in so many words "we aren't protecting the landlords' claim to their property, do what you will". The peasants then independently seized the land, usually either killing or driving out the landlord, and distributed it among themselves or sometimes held it in common.

There's an interesting relation between this approach and Mao's observations of peasant movements a few decades prior.