What that paper says is that 'large, corporate' farms perform worse than 'small, individual' ones. And it explicitly says "The different behavior may be understood if we recall that in our samples scale is a proxy for farm type.".
What performs better are individual-run farms, i.e. not collectives (which is pertinent in the paper because that style of farming is a holdover from Communist times) and not what is called 'corporate' farming in the paper where you have a bunch of MBA's and agronomists hiring cheap labor.
Essentially (going beyond the numbers of the paper), farms that are run by individuals who have (presumably) more 'skin in the game' and who know the land, the history and local conditions better than hired guns is what makes those farms more productive. But that also puts a cap on the maximum amount of land you can manage, hence the correlation between farm organizational type and its size.
So, to tie that back to the GP - it's true that it's not necessarily the 'megafarms' that he's at a competitive disadvantage to (depending on what market you're looking at - I mean a farm as small as that isn't competing for big Cargill contracts), but his mostly tradition-based management style (looking at the description of the ground egg shells) did put him at a disadvantage to the point that such farmers can't survive today. Today's farmers are agricultural engineers (more often than not literally - many farmers, and a growing percentage, have some sort of university education). Keeping a farm profitable today is about leveraging technology, keeping data very accurately and making the most of it. That includes local-scale sensor networks, microdosage of nutrients ('fertilizers'), very fine-grained crop rotation schemes. And in lifestock and dairy farming even more so. It's all romantic that GP's grandfather had bunch of chickens and some cows that he could milk by hand if he wanted to, but the economic reality is that no dairy farmer today can survive that way, regardless of farm size.